President Obama made a crucial tactical shift on Tuesday as he offered a full-throated appeal for immigration reform, embracing the plan cobbled together by a group of senators from both parties.

Despite predictions that Obama would unveil a significantly more liberal approach than the group led by John McCain, Marco Rubio, and Chuck Schumer, he made the calculation that having big-name Republicans on board could break the logjam on Capitol Hill.

Speaking from Las Vegas, the president wasted little time praising “a bipartisan group of senators announced their principles for comprehensive immigration reform, which are very much in line with the principles I’ve proposed and campaigned on for the last few years.” Translation: I’m on board.

But Obama also wielded a stick, saying if Congress doesn’t act quickly, he would send up his own bill.

Obama spoke of the 11 million illegal immigrants by saying “yes, they broke the rules,” but can no longer be allowed to “live in the shadows.” And he said the “pathway to citizenship” he would create would require those here illegally to go to the “back of the line,” behind legal applicants.

“It won’t be a quick process, but it will be a fair process, and will lift these individuals out of the shadows.” With that single sentence, he mirrored the Senate approach.

Obama made a bow toward greater enforcement but stressed the need to think of immigrants as human beings, not an abstract problem.

The major question now is whether John Boehner’s House will be receptive to a compromise approach after an election in which Mitt Romney performed miserably among Hispanic voters.

The key element of the Senate proposal is that while the nation’s illegal immigrants would in effect be legalized, they would not be able to become citizens until border security and employer verification of immigration status are beefed up. Only then would those here illegally be able to pursue citizenship by paying a fine and back taxes.

The Washington Post, citing an unnamed administration official, reported Tuesday morning that Obama would call for a faster and more straightforward path to citizenship for undocumented workers and students, out of concern that a cumbersome process could create delays that could last for decades. But Obama did not do that.

He made a pitch for how reform would help the economy, saying that Intel and Instagram were created by immigrants who came here and stayed.

This may be a rare moment when the stars are aligned. What passes for the Republican establishment, including such figures as Karl Rove, is lining up behind the Senate plan. McCain, who has frequently been at odds with Obama since losing to him in 2008, seems prepared to play the kind of dealmaking role that was his signature before his second presidential campaign. And Obama faced little backlash last year after suspending enforcement against illegal immigrants under 30 who were brought to the U.S. when they were under 16.

But immigration reform has proved utterly elusive since 1986, when Ronald Reagan and congressional Democrats passed a law aimed at what were then the 3 million illegal immigrants in the country. George W. Bush tried, and failed, to muscle a bill through Congress, but the GOP has taken a sharp turn toward harsher rhetoric in recent years—at least until Obama won reelection.

In a bit of deft maneuvering, the Senate gang of eight—which includes Linsdey Graham and Dick Durbin—announced its agreement on Monday, getting out ahead of Obama’s speech. Had the president put forth a substantially different plan, he would have undermined the Senate effort and complicated the political salesmanship.

But many House Republicans view any path to legalization as a form of amnesty for those who broke the law. “This will be the end of the Republican Party if it passes,” GOP Rep. Lou Barletta told The Daily Beast earlier.

The lingering question is whether enough House conservatives will follow the lead of their Senate counterparts in an environment in which the party is becoming increasingly less competitive with a fast-growing demographic.

Rubio, the son of Cuban-American immigrants, could provide cover for Republicans who fear being perceived as soft on the issue. Rubio hailed the gang of eight’s agreement for its “straightforward principle” that “we have to modernize our legal immigration system, we have to have a real enforcement mechanism to ensure we’re never here again in the future, and we have to deal with the people that are here now in a way that’s responsible but humane.”

With a budget deal far from certain and the prospects for gun-control legislation daunting at best, immigration reform may offer Obama his best chance of a major second-term achievement.