Potential Senate roadblocks center on how to structure the avenue to citizenship and on whether legislation would cover same-sex couples - and that's all before a Senate measure could be debated, approved and sent to the Republican-controlled House where opposition is sure to be stronger.
Obama, who carried Nevada in the November election with heavy Hispanic support, praised the Senate push, saying Congress is showing "a genuine desire to get this done soon." But mindful of previous immigrations efforts that have failed, he warned that the debate would be difficult and vowed to send his own legislation to Capitol Hill if lawmakers don't act quickly.
"The question now is simple," Obama said during a campaign-style event in Las Vegas, one week after being sworn in for a second term in the White House. "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."
Shortly after Obama finished speaking, cracks emerged between the White House and the group of eight senators, which put out their proposals one day ahead of the president. Florida Sen. Marco Rubio, a potential 2016 presidential candidate, faulted Obama for not making a citizenship pathway contingent on tighter border security, a central tenet of the lawmakers' proposals.
"The president's speech left the impression that he believes reforming immigration quickly is more important than reforming immigration right," Rubio said in a statement.
House Speaker John Boehner also responded coolly, with spokesman Brendan Buck saying the Ohio Republican hoped the president would be "careful not to drag the debate to the left and ultimately disrupt the difficult work that is ahead in the House and Senate."
Despite possible obstacles to come, the broad agreement between the White House and bipartisan lawmakers in the Senate represents a drastic shift in Washington's willingness to tackle immigration, an issue that has languished for years. Much of that shift is politically motivated, due to the growing influence of Hispanics in presidential and other elections and their overwhelming support for Obama in November.
The separate White House and Senate proposals focus on the same principles: providing a way for most of the estimated 11 million people already in the U.S. illegally to become citizens, strengthening border security, cracking down on employers who hire illegal immigrants and streamlining the legal immigration system.
A consensus around the question of citizenship could help lawmakers clear one major hurdle that has blocked previous immigration efforts. Many Republicans have opposed allowing illegal immigrants to become citizens, saying that would be an unfair reward for people who have broken the law.
Details on how to achieve a pathway to citizenship still could prove to be a major sticking point between the White House and the Senate group.
Obama and the Senate lawmakers all want to require people here illegally to register with the government, pass criminal and national security background checks, pay fees and penalties as well as back taxes and wait until existing immigration backlogs are cleared before getting in line for green cards. Neither proposal backs up those requirements with specifics.
After achieving legal status, U.S. law says people can become citizens after five years.
The Senate proposal says that entire process couldn't start until the borders were fully secure and tracking of people in the U.S. on visas had improved. Those vague requirements would almost certainly make the timeline for achieving citizenship longer than what the White House is proposing.
The president urged lawmakers to avoid making the citizenship pathway so difficult that it would appear out of reach for many illegal immigrants.
"We all agree that these men and women have to earn their way to citizenship," he said. "But for comprehensive immigration reform to work, it must make clear from the outset that there is a pathway to citizenship."
"It won't be a quick process, but it will be a fair process," Obama added.
Another key difference between the White House and Senate proposals is the administration's plan to allow same-sex partners to seek visas under the same rules that govern other family immigration. The Senate principles do not recognize same-sex partners, though Democratic lawmakers have told gay rights groups that they could seek to include that in a final bill.
John McCain of Arizona, who is part of the Senate immigration group, called the issue a "red flag" in an interview Tuesday on "CBS This Morning."
Washington last took up immigration changes in a serious way in 2007, when then-President George W. Bush pressed for an overhaul. The initial efforts had bipartisan support but eventually collapsed in the Senate because of a lack of GOP support.
Cognizant of that failed effort, the White House has readied its own immigration legislation. But officials said Obama will send it to the Hill only if the Senate process stalls.
Most of the recommendations Obama made Tuesday were not new. They were included in the immigration blueprint he released in 2011, but he exerted little political capital to get it passed by Congress, to the disappointment of many Hispanics.
Some of the recommendations in the Senate plan are also pulled from past immigration efforts. The senators involved in formulating the latest proposals, in addition to McCain and Rubio, are Democrats Charles Schumer of New York, Dick Durbin of Illinois, Robert Menendez of New Jersey and Michael Bennet of Colorado, and Republicans Lindsey Graham of South Carolina, and Jeff Flake of Arizona.
Also Tuesday, in another sign of Congress' increased attention to immigration issues, a group of four senators introduced legislation aimed at allowing more high-tech workers into the country, a longtime priority of technology businesses. The bill by Republicans Rubio and Orrin Hatch and Democrats Amy Klobuchar and Chris Coons would increase the number of visas available for high-tech workers, make it easier for them to change jobs once here and for their spouses to work and aim to make it easier for foreigners at U.S. universities to remain here upon graduation.
Julie Pace reported from Washington. Associated Press writer Erica Werner contributed to this report.