It was a sign not only of eagerness among the Republicans to reach a deal, but also of the awareness that the political window opened by the election could slam shut.
"We all know we need to address this issue," McCain said. He believed that November clearly demonstrated that immigration reform was important to Latino voters and, if the GOP continued to thwart it, red states with growing Latino populations, including Arizona, would turn blue.
"Very few things get your attention as elections do," McCain said.
The senators met six times. At the sixth meeting, they agreed to a list of accepted principles that they would make public before their self-imposed Feb. 1 deadline. But the next day, Thursday, Jan. 24, news leaked that Obama would deliver a major speech on immigration on Jan. 29.
The Republican senators worried that Obama would stake out territory that would alienate their party.
Neither Democrats nor Republicans in the group had much, if any, contact with the administration. The White House was skeptical that the senators could reach accord, they believed, and the group did not know whether the president was preparing to unveil his own proposal.
The next day, Friday, members of the Congressional Hispanic Caucus met with Obama at the White House. They warned that he could jeopardize GOP support for negotiations underway in the House and Senate.
Obama was noncommittal, congressional and White House aides said.
The Senate staff raced through the weekend to write up the principles that the six senators had agreed on. Two more senators — a Republican and a Democrat — came on board. And the group shifted gears, planning to unveil the package on Monday, the day before the president's speech.
On Sunday night, Durbin was at a birthday party in Springfield, Ill. He'd had a glass of wine and was thankful he hadn't had more after he found out he needed to join a conference call that was being set up with Schumer and the president.
Durbin and Schumer, who was in New York, told Obama they had decided to announce their proposals on Monday and were optimistic they could turn them into legislation by March.
"I don't care that you go first; it doesn't bother me," Obama told the senators, as Durbin recalled the conversation. "I'm going to come out with my principles. And I'm also going to put the heat on you to do something. I don't want this to drag on. I want you to do something."
Obama told the senators he had a bill ready to send to Congress, but he assured them he would stand down. But if they didn't act, he promised, he would send his bill to Congress.
Good, the senators agreed; political pressure would help.
On Tuesday evening, after Obama gave his speech at a high school in Las Vegas, the senators met again, arrayed on couches and overstuffed chairs in McCain's office suite.
McCain came in, in a cheerful mood.
"Well, that wasn't so bad," the Arizona senator said.
Rubio also had upbeat news. He had been on Rush Limbaugh's show, and the influential conservative host had told him what he was doing was "admirable and noteworthy."
Then, the senators turned to the details, which could determine whether their work writes another chapter in the nation's fitful attempts to deal with its millions of illegal immigrants — or closes the book.
Michael A. Memoli in the Washington bureau contributed to this report.