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.”