But both the White House and Senate proposals for tackling the complex and emotionally charged issue still lack key details. And potential roadblocks are already emerging over how to structure the road to citizenship and whether a bill would will same-sex couples — and that’s all before a Senate measure can be debated, approved and sent to the Republican-controlled House where opposition is likely to be stronger.

Obama, in the heart of the heavily Hispanic Southwest, said Congress is showing “a genuine desire to get this done soon.” But mindful of previous immigrations efforts that have failed, Obama warned that the debate would become more difficult as it gets closer to a conclusion.

“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.”

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, which is comprised of eight lawmakers — four Democrats and four Republicans.

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. After reaching that 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.