President Barack Obama waves as he arrives to speak about immigration at Del Sol High School, Tuesday, Jan. 29, 2013, in Las Vegas. Photo: Carolyn Kaster, Associated Press Photo:

President Barack Obama waves as he arrives to speak about immigration at Del Sol High School, Tuesday, Jan. 29, 2013, in Las Vegas. Photo: Carolyn Kaster, Associated Press Photo:

LAS VEGAS — Declaring “now is the time” to fix broken immigration laws, President Barack Obama on Tuesday unveiled his plan for putting millions of illegal immigrants on a pathway to citizenship, including allowing U.S. citizens and permanent residents to sponsor a visa for a same-sex partner.

But already, potential roadblocks have emerged over how to structure the road to citizenship and whether a Senate bill introduced Monday would eventually include same-sex, binational couples.

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 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.

But a 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:

From a fact sheet released by the White House:

Keep Families Together. The proposal seeks to eliminate existing backlogs in the family-sponsored immigration system by recapturing unused visas and temporarily increasing annual visa numbers. The proposal also raises existing annual country caps from 7 percent to 15 percent for the family-sponsored immigration system. It also treats same-sex families as families by giving U.S. citizens and lawful permanent residents the ability to seek a visa on the basis of a permanent relationship with a same-sex partner. The proposal also revises current unlawful presence bars and provides broader discretion to waive bars in cases of hardship.

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.

“The president has long believed that Americans with same-sex partners from other countries should not be faced with the painful choice between staying with the person they love or staying in the country they love,” said White House spokesman Jay Carney, earlier today.

But Sen. John McCain (R-Ariz.) called the issue a “red flag” in an interview Tuesday on “CBS This Morning.” McCain said he didn’t think the issue was of “paramount importance at this time.”

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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.

Associated Press contributed to this report.