"They'll never be satisfied," he said.
Stymied by both chambers of Congress, the president ditched lawmakers in favor of voters who might pressure them, making an appeal to the public on a hot and dusty day far outside Washington. He told a friendly El Paso crowd that it's up to them to tell Congress to pass legislation providing a pathway to citizenship for 11 million illegal immigrants.
The approach also allowed the president to make clear that it's Republicans - not him - standing in the way of immigration legislation. As his re-election campaign approaches it's a message he wants broadcast loud and clear to Latino voters who don't like his administration's heavy deportations and feel he never made good on his promise to prioritize immigration legislation during his first year in office.
"I am asking you to add your voices to this," Obama said. "We need Washington to know that there is a movement for reform gathering strength from coast to coast. That's how we'll get this done."
Countering Republican calls to focus on border security before moving to a comprehensive overhaul, Obama boasted of increasing Border Patrol agents, nearing completion of a border fence and screening more cargo, among other steps.
"We have gone above and beyond what was requested by the very Republicans who said they supported broader reform as long as we got serious about enforcement," Obama said. "But even though we've answered these concerns, I gotta say I suspect there are still going to be some who are trying to move the goal posts on us one more time."
"Maybe they'll need a moat," he said derisively to laughter from the crowd. "Maybe they'll want alligators in the moat."
"The question is whether those in Congress who previously walked away in the name of enforcement are now ready to come back to the table and finish the work we've started," he said.
Obama also tailored his argument to the times, making his case for immigration reform in newly sharpened economic terms. He said the middle class would benefit from bringing illegal immigrants out of an underground economy and drawing on the abilities of immigrants educated at American universities. Obama also noted that it's not just Latinos who want an immigration remake, but also police chiefs, business owners, educators and others.
His speech broke no new policy ground, though, and he declined to offer a bill or call on Congress to send him one by a particular deadline - a bow to political realities on Capitol Hill. Republicans who control the House are hostile to overhaul legislation.
And as if to underscore how faintly his call for immigration reform would resonate in Congress, two key border state Republicans immediately responded with a statement demanding to know: "President Obama speaks about our broken immigration system; but what about our broken borders?" The statement was from Republican Sens. Jon Kyl and John McCain of Arizona, the latter Obama's 2008 presidential opponent and a one-time supporter of comprehensive overhaul legislation.
Obama's personal pitch was the latest step in a visible campaign to build support and pressure on Republicans to act. He went so far as to encourage people to sign up to help him at the White House website. He said it was up to the American people to drive the debate and isolate areas where both parties can agree.
Politically, Obama sought to have it both ways.
He said he would lead a "constructive and civil debate" on the issue but publicly questioned the motives of Republicans and their ability to keep their word.
And it remained unclear how mocking Republican calls for border security would get Obama any closer to his goal of bipartisan legislation.
Just across the Rio Grande from the Chamizal National Park, where Obama spoke, the Ciudad Juarez park has been used by criminals to dump the bodies of rivals. A nearby entertainment district, within sight of a major bridge into the United States, has been the scene of numerous shootouts among rival cartels and authorities.
The president made his pitch in a state he lost by more than 10 percentage points in 2008 and is unlikely to pick up in 2012. But Hispanic voters are critical to the president's re-election. Latinos accounted for more than 7 percent of voters in the 2008 presidential election, according to the Pew Hispanic Center, and their numbers are greater in certain swing states like Nevada, New Mexico, Colorado and Florida.
The trip had a more overtly political component too. From El Paso, the president headed to the relatively liberal bastion of Austin to raise money for the Democratic National Committee at two events. A total of about 800 people paid $44 to $35,800 to attend.
The president wasn't able to get immigration legislation through Congress last year that would have provided a route to legal status for college students and others who were brought to the country as children. The so-called DREAM Act passed the House, then controlled by Democrats, but was blocked by Senate Republicans.
The Senate is now even more heavily Republican, and Republicans control the House. That means immigration reform can't happen unless they cooperate. Nonetheless, Senate Democrats plan to reintroduce the DREAM Act on Wednesday, with their counterparts in the House following suit. Given Republican opposition the bills likely won't get far, but Obama will try to make certain voters know who to blame.
Erica Werner reported from Washington. Associated Press writers Ben Feller, Suzanne Gamboa, Jim Kuhnhenn and Alicia Caldwell in Washington contributed to this report.