And yet a sweeping, bipartisan Senate immigration bill is on the brink of death this week in the more conservative House of Representatives, eight months after Obama handily won the second term many of those same Republicans had vowed to deny him.
"We are not going to do the Senate bill," John Boehner, Republican speaker of the House of Representatives, told a Capitol Hill news conference on Thursday, a day after he privately urged his caucus to embrace immigration reform.
"I'm much more concerned about doing it right than I am about meeting some deadlines."
The biggest stumbling block for House Republicans is providing a path to citizenship for the 11 million immigrants currently living illegally in the United States. The lawmakers consider it amnesty, something vehemently opposed by the most conservative Republicans, and they want to see far tougher border security and employment verification measures than called for in the Senate bill.
Obama met Thursday with two of the senators who hammered out bipartisan consensus last month to come up with the type of comprehensive immigration reform the president is hoping will be a hallmark of his second term.
Arizona Sen. John McCain, Obama's opponent in the 2008 election, told reporters that the president wasn't exerting unreasonable pressure on Congress.
"These members, these Republican House members — many of them are in districts they'll be representing for a long time — do not feel that they have been unduly pressured by the president of the United States," McCain said.
"So I think the president is walking a careful line here, and I think it's the appropriate one."
That's a starkly more conciliatory tone than the statement put out a day earlier by House Republicans after the party's leadership tried to convince the rank and file of the benefits of immigration reform amid bitter divisions within the GOP over the issue.
House Republicans "don't trust a Democratic-controlled Washington, and they’re alarmed by the president's ongoing insistence on enacting a single, massive, Obamacare-like bill rather than pursuing a step-by-step, common-sense approach to actually fix the problem," their statement read.
Boehner and Paul Ryan, Mitt Romney's running mate in last year's election, reportedly urged their colleagues to pass immigration reform legislation during the tense closed-door meeting. Boehner told them the party would be "in a much weaker position" if it failed to act.
Yet House Republicans emerged from the meeting with a bleak reality check for those hoping for a sweeping overhaul of the country's immigration system, saying they rejected the Senate approach and would attempt to take slower, piece-by-piece steps.
Boehner seemed keen to present a united front in his news conference on Thursday, despite tensions behind the scenes. He said that the "vast majority" of House Republicans support immigration reform.
"Through all the conversations that have occurred, with my own members, with Democrat members, it's clear that dealing with this in bite-sized chunks that members can digest and that the American public can digest is the smartest way to go," he said.
House Republicans, meantime, were reaching across the aisle to Democrats to gauge their support of such a piecemeal approach.
Republicans are attempting to assess precisely what Democrats in the House would be willing to support when immigration comes to the floor, which isn't likely to happen until September at the earliest. They're hoping for bipartisan backing for House bills that would overhaul the country's employment verification system as well as toughen border security — legislation that would counter the Senate's legislative efforts.
"We do the right policy and the politics will follow," said Republican Raul Labrador, a Latino congressman from Idaho who's opposed to the Senate bill.
"But I do agree that we have to, as a party, go out to the communities and talk to them, explain to them why our policies are different than their policies. Ask them why they think that under the Obama administration there are more Hispanic people that are poor, there’s more African-Americans poor, there’s more people losing their job, their businesses."
That argument didn't wash with Hispanic and African-American voters last year, however, when Romney routinely made it while on the campaign trail.
Time is of the essence for immigration reform. Legislators leave D.C. in August for the annual summer recess, and often face angry voters at town hall meetings in their districts. Those in ultra-conservative districts are likely to face opposition to any notion of granting illegal immigrants a path to citizenship.
If immigration reform doesn't pass this year, its prospects will grow even dimmer in 2014, when all House members face re-election in the mid-term congressional elections.
“If it doesn't happen in this year, then it's unlikely it's going to happen in an election year,” Nancy Pelosi, House minority leader, said Thursday.
She chided Republicans for failing to act swiftly, arguing party faithful that include law enforcement officials, business representatives and religious voters are in favour of immigration reform.
"They have been very enthusiastic over time and getting impatient about Congress taking action," she said. "It would be a real failure on our part if we could not find a path to go to conference to air our differences to come up with a bill."