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Mr. Obama did not try to outbid the deal and, in fact, said the deal was “very much in line” with what he supports.

His own principles, which the White House released in a fact sheet, are more detailed than the five-page framework that the senators released Monday. The brevity of the plans underscores the many hurdles that remain as both sides try to write legislation that is likely to run hundreds of pages long.

One of those hurdles emerged Tuesday: how to handle gay couples in the immigration system.

Sen. John McCain of Arizona, who led Republicans in negotiations on the framework, said their plan was silent on that issue but that extending full immigration marriage benefits to same-sex couples would be “a red flag” for him.

Mr. Obama supports extending immigration benefits to same-sex couples, spokesman Jay Carney said.

“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,” Mr. Carney told reporters traveling on Air Force One to Las Vegas.

That drew praise from Rep. Michael M. Honda, California Democrat, who has fought for years to extend immigration benefits to gay couples.

Mr. Obama, who late last year said he would write his own immigration bill, backed off that vow Tuesday, saying he would give Congress a chance to work out a deal.

“But it’s important for us to recognize that the foundation for bipartisan action is already in place. And if Congress is unable to move forward in a timely fashion, I will send up a bill based on my proposal and insist that they vote on it right away,” he said.

Sen. Charles E. Schumer, the Democrat who is leading the bipartisan group of eight senators along with Mr. McCain, said Mr. Obama handled his speech perfectly.

“He is using the bully pulpit to focus the nation’s attention on the urgency of immigration reform and set goals for action on this issue. But he is also giving lawmakers on both sides the space to form a bipartisan coalition,” Mr. Schumer said.

In his remarks, Mr. Obama said more action needs to be taken on border security but touted the progress made by his administration and that of his predecessor, George W. Bush.

“We put more boots on the ground on the southern border than at any time in our history. And today, illegal crossings are down nearly 80 percent from their peak in 2000,” he said.