A senior administration official said the speech was the start of a concerted campaign to force Republicans to follow through on the bipartisan proposal. He predicted that given the president’s popularity with Hispanic voters, they would find it hard vote down a bill with his name on it.

Mr. Obama offered a familiar list of proposals: tightening security on borders, cracking down on employers who hire illegal immigrants and temporarily issuing more visas to clear the huge backlog of people applying for legal status in the country.

His speech, on the heels of the bipartisan Senate proposal, sets the terms for one of the year’s landmark legislative debates. These are only the opening steps in a complicated dance, and both the politics and the policy can be treacherous ground, as shown by the failed effort to overhaul immigration laws in the George W. Bush administration.

But the flurry of activity underscores the powerful new momentum behind an overhaul of the system, after an election that dramatized the vulnerability of Republicans on the issue, with Mr. Obama piling up lopsided majorities over Mitt Romney among Hispanic voters.

“Most Americans agree that it’s time to fix a system that’s been broken for way too long,” Mr. Obama said to an audience of about 2,000 high school students, many of them Hispanic. They applauded loudly when he mentioned the Dream Act, which offers amnesty to children of immigrants who are in the United States illegally.

In scrambling to present their blueprint on Monday, the day before Mr. Obama’s speech, the senators stole a march on the president. But their intent appeared less to undermine his efforts than to stake out their own role in drafting a comprehensive bill.

“It is a fascinating Washington horse race that you don’t always see, and a signal of the seriousness to get across the finish line,” said Angela Kelley, an expert on immigration at the Center for American Progress, a liberal research group.