"He reminds me that we are playing a long game here ... and that change is hard, and change is slow and it never happens all at once," she told a nation impatient with slow economic progress and persistently high unemployment of 8.3 percent. "But eventually, we get there, we always do," she said in a speech that roused Democrats packed into their convention arena and blended scenes from almost 20 years of marriage with the Obamas' time in the White House.
Mrs. Obama, given a huge ovation and emotionally describing herself as the "mom in chief," made no mention of Republican challenger Mitt Romney. But those who preceded her to the podium on the first night of the president's convention were scathing.
"If Mitt was Santa Claus, he'd fire the reindeer and outsource the elves," declared former Ohio Gov. Ted Strickland in one biting speech.
Tapped to deliver the keynote address, San Antonio Mayor Julian Castro said Romney was a millionaire politician who "quite simply, doesn't get it" when it comes to the needs of the middle class. Referring to the Republican's support for mandatory health insurance when he was governor of Massachusetts, he added, "Gov. Romney has undergone an extreme makeover, and it ain't pretty."
Polls made the race for the White House a tight one, almost certain to be decided in a string of eight or 10 battleground states where neither the president nor Romney holds a clear advantage. There was ample evidence during the day of an underperforming economy, including a report that said manufacturing activity declined for a third straight month and an announcement from the Treasury that the government's debt exceeded $16 trillion at the close of the business day.
Delegates cheered as a parade of speakers extolled Obama's support for abortion rights and gay marriage, for consumer protections enacted under his signature health care law and for the auto industry bailout he won from Congress in his first year in office.
"He said he'd take out bin Laden, and with our great SEAL team, he did," declared former Virginia Gov. Tim Kaine in one of several references to the military raid that ended the life of the terrorist mastermind behind the attacks of Sept. 11, 2001.
There was no end to the appeals for donations to Obama's re-election campaign, falling further behind Romney in cash on hand with each passing month. "If you think Barack's the right man for the job, please show your support with a donation of $5 or more today," the first lady emailed supporters a little more than 90 minutes before her speech.
She walked out to the crowd's cheers as the band played Stevie Wonder's "Signed, Sealed, Delivered I'm Yours," the song he sang onstage at Obama's Denver convention four years ago.
The president was back home in the White House after a campaign appearance in Virginia as delegates cheered every mention of his name from the convention podium. He and their daughters watched on television as Mrs. Obama spoke.
"Believe it or not, when we were first married, our combined monthly student loan bills were actually higher than our mortgage," she told the convention. "We were so young, so in love and so in debt."
She confided that at family dinners in the White House with her and their daughters, the president joins in "strategizing about middle school friendships."
Mrs. Obama's poll numbers are better than her husband's, and her speech was aimed at building support for him, much as Ann Romney's remarks at last week's Republican National Convention were in service to her husband's presidential ambitions.
"When it comes to rebuilding our economy, Barack is thinking about folks like my dad - who worked at a municipal water plant - and his own grandmother, a bank secretary," the first lady said.
Referring to her own children as well as those of others, she said, "If we want to give them that sense of limitless possibility, that belief that here in America there is always something better out there if you are willing to work for it, then we must ... stand together for the man we can trust to keep moving this great country forward, my husband, our president, President Barack Obama."
The weak economy hung over the convention as it dominates the election.
Obama "knows better than anyone there's more hard work to do" to fix it said Castro. He said that after the deep recession, the nation is making progress "despite incredible odds and united Republican opposition."
He declared that 4.5 million jobs have been created since the president took office - though that number refers only to private sector employment gains over the past 29 months and leaves out state and local government jobs that continue to disappear each month.
Castro, the first Hispanic chosen to deliver a keynote address, was introduced - to the delight of the crowd - by his identical twin brother, Joaquin, a candidate for Congress. The mayor was unsparing in criticizing Romney, suggesting the former Massachusetts governor might not even be the driving force on the Republican ticket this fall.
"First they called it 'trickle down, the supply side," he said of the economic proposals backed by Republicans. "Now it's Romney/Ryan. Or is it Ryan/Romney?"
"Either way, their theory has been tested. It failed. ...Mitt Romney just doesn't get it," Castro said. Romney's running mate is Wisconsin Rep. Paul Ryan.
The divide over taxes goes to the core of the campaign.
Romney and the Republicans favor extension of all of the existing Bush-era tax cuts due to expire on Dec. 31, and also want to cut tax rates 20 percent across the board.
Obama, too, wants to keep the existing tax cuts in place - except for people with earnings of $250,000 a year or more.
Democrats criticized Romney last week for failing to offer a detailed plan to fix the economy. But nowhere in their own convention's first evening of speechmaking did anyone present proposals for reining in deficits that now exceed $1 trillion annually.
Delegates in the convention hall cheered whenever Obama's image showed on the huge screen behind the speaker's podium, and roared when the late Sen. Edward M. Kennedy was shown mocking Romney in their 1994 Senate race.
"On the issue of choice, I am pro-choice, my opponent is multiple choice," the late senator said as cheers grew louder.
Romney supported abortion rights while serving as governor; he opposes them now.
Democrats unspooled insult after insult as they took their turn the week after the Republicans had their convention in Tampa, Fla.
Illinois Gov. Pat Quinn said that Republicans had omitted mention of Romney's term as Massachusetts governor at their gathering.
"We already knew this extremely conservative man takes some pretty liberal deductions. Evidently that includes writing off all four years he served as governor," Quinn declared.
Said Senate Majority Leader Harry Reid of Nevada, speaking of Romney: "Never in modern American history has a presidential candidate tried so hard to hide himself from the people he hopes to serve."
"When you look at the one tax return he has released, it's obvious why there's been only one. We learned that he pays a lower tax rate than middle-class families. We learned he chose Swiss bank accounts and Cayman Island tax shelters over American institutions."
Obama, by contrast, was lauded for helping win approval of health care legislation and for supporting abortion rights and gay marriage.
In his campaign trip to Virginia earlier in the day, Obama told an audience at Norfolk State University that the economy will get worse if Romney wins the White House this fall and that Election Day apathy was his enemy - and theirs.
Republicans are "counting on you, maybe not to vote for Romney, but they're counting on you to feel discouraged," he said. "And they figure if you don't vote, then big oil will write our energy future, and insurance companies will write our health care plans, and politicians will dictate what a woman can or can't do when it comes to her own health."
On the final stop of a pre-convention campaign circuit of several battleground states, the president also dropped off a case of White House-brewed beer at a local fire station.
The Republican challenger was in Vermont as the Democratic convention began, preparing for three fall debates with Obama almost certain to be critical to the outcome of the election.
There was no shortage of political calculation behind the program of the convention's first night - or for any other.
Democratic delegates bestow their nomination on Obama and Vice President Joe Biden on Wednesday, the same night former President Bill Clinton delivers a prime-time speech aimed at voters disappointed with the results of the past four years yet undecided how to cast their ballots.
White men favor Romney over Obama in public and private polls, but a Gallup survey taken in July showed that 12 years after leaving office, Clinton was viewed favorably by 63 percent of the same group and unfavorably by only 32 percent.
Obama's acceptance speech caps the convention on Thursday night at the 74,000-seat Bank of America football stadium. Aides kept a wary eye on the weather in a city that has been hit in recent days with strong afternoon rains.
Republicans did their best to rain on Obama's convention, whatever the weather.
Vice presidential candidate Paul Ryan spoke in Westlake, Ohio, standing behind a lectern bearing a sign that read "Are you better off?"
Republicans released a web video that interspersed images of Obama and the economy's weak performance with slightly out-of-focus video clips of former President Jimmy Carter discussing the nation's economic woes when sat in the Oval Office more than 30 years ago.
Matthew Daly reported from Norfolk, Va. Associated Press writers Steve Peoples in Ohio, Kasie Hunt in Vermont, Jack Gillum and Tom Raum in Washington, Thomas Beaumont in Des Moines, Iowa, and Ken Thomas and Matt Michaels in Charlotte contributed.