President Barack Obama said Tuesday that long-sought reforms to a "broken" immigration system were within America's grasp, seeking to lock in rare momentum towards a major cross-party compromise.

Obama laid out his principles on the divisive issue, which would nudge 11 million illegal immigrants slowly towards citizenship within stronger US borders and allow prized foreign students to stay on after graduation to boost the US economy.

"The question now is simple. Do we have the resolve as a people, as a country, as a government, to finally put this issue behind us? I believe that we do," Obama said, during a lightning stop in Las Vegas, Nevada.

"I believe we are finally at a moment where comprehensive reform is within our grasp," Obama said, at a time when Republicans are seeking to mitigate Democratic primacy among Hispanic voters, for whom immigration is a key issue.

"Now is the time. Now is the time. Now is the time," Obama said.

The president sought to harness signs of unusual consensus in sharply divided Washington over immigration reform, six years after the last attempt to overhaul the system ended in a spectacular and politically toxic failure.

His speech came a day after a bipartisan group of senators unveiled their own guidelines for legislation on an issue that would represent a major legacy achievement for Obama at the start of his final White House term.

The president noted that his immigration plan, first unveiled in detail in 2011, covered similar ground as the Senate approach.

Both plans would broadly:

-- Offer illegal immigrants a long path to permanent residency and citizenship, requiring them to pay back taxes, learn English, have background checks and demonstrate familiarity with US culture

-- Include efforts to strengthen US borders and visa systems and speed a path out of limbo by young people brought to the country illegally by their parents.

-- Improve worker verification systems that deter illegal immigration and dismantle barriers to highly skilled foreign workers entering America to catalyze future economic growth.

But there are some major and politically problematic differences:

-- The Senate plan makes the scheme offering a route to citizenship contingent on the completion of certain enforcement measures. Obama's would not.

-- The president's plan also treats same sex couples the same as straight ones -- ie, a US citizen's same sex partner would have the same rights to come to America as another person's straight spouse.

Both differences are a possible irritant as the White House and Republicans seek a compromise, both sides hope, by later this year.

One prominent Republican, rising star Marco Rubio -- who may run for president in 2016 -- said Tuesday he would not back any bill that did not include a "trigger mechanism" for enforcement.

"If this endeavor becomes a bidding war to see who can come up with the easiest, quickest and cheapest pathway to a green card possible, this thing is not going to go well, folks," Rubio said.

Republicans are sensitive to any claims by their conservative base voters that the path to citizenship equates in any way to "amnesty," an explosive charge which contributed to the failure of immigration reform in 2007.

While reflecting hope, Obama displayed his customary impatience with the inertia that often descends on Congress, promising that if lawmakers did not act within a "timely" manner, he would send up his own bill and demand a vote.

Reactions to the speech reflected hopeful caution that change could be at hand.

Senator John McCain, a key Republican player, said he appreciated Obama's support for the Senate plans, and stressed that border security enforcement was particularly important.

Fellow Arizona Senator Jeff Flake warned Obama that the enforcement trigger was necessary to getting immigration reform through Congress.

Brendan Buck, a spokesman for Republican House Speaker John Boehner, advised Obama not to "drag the debate to the left," in a sign that the party leadership faces a tough sell on immigration reform to some of its members.

Key Democratic Senator Chuck Schumer complimented the president for handling the issue "perfectly" by stressing urgency while allowing both sides space to form a coalition.

Treacherous politics dashed similar reform efforts under president George W. Bush, but the rising muscle of Hispanic voters has shifted political calculations and created the most favorable climate for reform in years.

Obama repeatedly promised during his first term to push immigration reform and successfully laid the blame on gridlock on Republicans who paid a heavy price as Hispanic voters flocked to the president last November.