But the numbers mask a more complicated reality: Obama and Democratic leaders have modest leverage over several pivotal Senate Democrats who are more concerned about their next election or feel they have little to lose by opposing their party's hierarchy.
One is still smarting from being forced to abandon next year's election. Another had to leave the Democratic Party to stay in office. And some are from states that Obama lost badly last year.
These factors will limit the president's ability to play his strongest card - an appeal for party loyalty and Democratic achievement - in trying to muster the 60 votes his allies will need this fall to overcome a Republican filibuster in the 100-member Senate.
When lawmakers face a tough vote, their uppermost thought is "survival," said Alan Simpson, a Wyoming Republican who spent three terms in the Senate.
On a very few occasions, Simpson said, then-President George H.W. Bush asked him to cast a vote likely to cause him political problems back home. That was perhaps three times in 18 years, said Simpson, who held a GOP leadership post. "I swallowed hard and went over the cliff," he said.
But it's a sacrifice that presidents and party leaders should not count on, he said.
The Democratic leaders' limited leverage will complicate the push for allowing the government to sell insurance in competition with private companies. Some Senate Democrats who oppose the idea are from states that voted heavily against Obama last fall.
Democratic Sen. Blanche Lincoln faces a potentially tough re-election race next year in Arkansas, where Obama lost to Republican John McCain by 20 percentage points. She says she will base her health care votes on what is best for Arkansans.
Choice and competition among insurers are good, Lincoln said, but "I've ruled out a government-funded and a government-operated plan."
Sen. Mary Landrieu of Louisiana, where Obama lost by a similar margin, said she might be willing to let some states try "fallback or trigger" mechanisms that would create a public option if residents don't have enough insurance choices.
But she told reporters, "I'm not for a government-run, national, taxpayer-subsidized plan, and never will be."
Another Democratic senator, who also may prove wary of Obama's overtures, takes the opposite stand.
"I would not support a bill that does not have a public option," said Sen. Roland Burris, D-Ill. "That position will not change."
Burris' willingness to bend could prove crucial this fall if Obama and Senate Majority Leader Harry Reid, D-Nev., need every possible vote in crafting a compromise, such as a national public option that is triggered if certain insurance availability targets aren't met.
But Burris may be in no mood to play ball. Obama and other top Democrats sharply criticized his appointment to the Senate in December by an ethically tainted governor, Illinois' Rod Blagojevich, and they forced Burris to abandon hopes of winning election in 2010 by making it clear they would not back him.
In short, Burris, 72, has virtually nothing to lose by defying his party's leaders and voting as he pleases.
Sen. Joe Lieberman of Connecticut is another potentially crucial senator with tenuous ties to the Democratic Party's hierarchy. Rejected by Connecticut's Democratic voters in the 2006 primary, he kept his Senate seat by running as an independent. He now calls himself an Independent Democrat.
Lieberman has criticized the health care bill that emerged from the Senate Finance Committee, but it and other health bills are undergoing changes.
Another centrist Democrat whose vote is uncertain is Sen. Evan Bayh of Indiana, a political battleground state.
"I want to know what works for families and small businesses," said Bayh, adding that he might back public insurance options run by states, not the federal government.
It's possible that Obama and party leaders eventually will ask Democrats such as Bayh, in the name of party loyalty, to vote to block a GOP filibuster of a health bill even if they plan to vote against the bill on final passage. The strategy might enable Democrats to muster the 60 votes needed on a crucial procedural question and then pass the bill with a simple majority.
Bayh said that if a party leader "is asking some of us to enable the passage of legislation that we think would be harmful to the people of our state, I don't think that's a fair thing to ask."
It's possible that centrist Democrats are holding out for favors from Obama and party leaders, such as pet projects for their states or help in their next campaign. Obama already has lavished special attention on some of them.
He invited Bayh to the White House last week for a chat about health care and the deficit. In an interview that led to good publicity back home, Bayh told Indiana reporters that the president "was asking for my leadership on both of those issues."