WASHINGTON — President Bush pushed ahead on Tuesday with his effort to bring Republicans in the House and the Senate together on a plan to reduce illegal immigration. But he ran into renewed resistance from conservatives who said they were not swayed by the case he made Monday to give many illegal workers a chance to become citizens.

The administration began an effort to build support for the president's approach, including putting Vice President Dick Cheney on Rush Limbaugh's syndicated radio program to try to mollify conservatives. Mr. Bush's plan combines a pledge of enhanced border security, backed by the deployment of up to 6,000 National Guard troops, with the creation of a temporary guest worker program and an opportunity for illegal immigrants who meet certain standards to gain legal status.

Mr. Bush spoke by telephone with the House speaker, J. Dennis Hastert of Illinois, and the Senate majority leader, Bill Frist of Tennessee, to press his argument, while other administration officials reached out to other lawmakers.

White House officials said they expected to work for months to build public support and win the votes on Capitol Hill to get a bill through the Senate and then to build a compromise with the House, which has already passed legislation that emphasizes border security and makes it a felony to be in the United States illegally.

Mr. Bush plans to travel to Arizona on Thursday to speak again about the issue, which he has now made a test of his political authority and one of the defining domestic initiatives of his second term. Karl Rove, Mr. Bush's strategist, is scheduled to meet privately on Wednesday morning at the Capitol with assembled House Republicans.

But a day after Mr. Bush delivered a nationally televised address on the issue from the Oval Office, there was little immediate evidence that he had bridged the deep divide in his own party or rallied public opinion sufficiently to break the impasse.

The House majority leader, John A. Boehner of Ohio, gave Mr. Bush credit for making a public effort on immigration and said he believed a final deal was possible. But, he said, "I don't underestimate the difficulty in the House and Senate coming to an agreement on this."

House conservatives said they saw little chance to reconcile the emerging Senate legislation and the House bill.

"The emphasis that he placed on the amnesty provision will not fly, especially in the House," said Representative Tom Tancredo, Republican of Colorado, who is one of the leaders of efforts to stop illegal immigration from Mexico and Central America.

Mr. Tancredo and other Republicans said their party was already facing a difficult midterm election. They said the party would suffer if the president successfully advanced his proposal, which they said diverged with public opinion and carried the risk of alienating much of the Republican base.

"It is a nonstarter with the American people, and the Republican Party will pay the price at the polls," said Representative Dana Rohrabacher, Republican of California.

Mr. Rohrabacher said that some fellow conservatives had found the president's address condescending and that the remarks "hinted at maliciousness on the part of those who are adamant that illegal immigration is bad for the country."

White House officials said they believed views would soften. "The issue is not going to thaw overnight with those with fairly entrenched positions," said Dan Bartlett, the White House counselor.

The Senate on Tuesday began working on its version, which roughly tracks Mr. Bush's approach.

In the first votes on the bill, senators sided with the president and advocates of comprehensive overhaul, rejecting by a vote of 55 to 40 a Republican proposal that the border be certified as secure by the Department of Homeland Security before new accommodations are made for immigrants.

"Enforcement first may be an attractive campaign slogan, but it is bad policy," said Senator Edward M. Kennedy, Democrat of Massachusetts and a member of the coalition behind the Senate's push for a broad bill that deals not only with new border enforcement but also with the estimated 11 million illegal residents of the United States.

Republicans in the House and some in the Senate warned that Senate approval of that approach could lead to a brutal clash with the House, where many Republicans steadfastly oppose any legislation that allows temporary workers or the prospect of citizenship for illegal residents.

"If this bill comes out with no major amendments, then I think we are in a true train wreck with the House," said Senator Saxby Chambliss, Republican of Georgia.

He and other Republicans said Mr. Bush's plan would be viewed as amnesty by many Americans, even if illegal immigrants had to pay fines and meet other requirements, because they would still be rewarded with legal status.

"Whether they say it is amnesty or not, it is amnesty when somebody here illegally gets a path to citizenship without going back to their home country," said Senator Tom Coburn, Republican of Oklahoma.

Mr. Bush and White House officials were emphatic Tuesday that the president would not approve legislation that did not include a guest worker provision and the "path to citizenship" that he outlined on Monday night. "I said I want a comprehensive bill," Mr. Bush said when a reporter began asking him whether he could abide by separate bills.

Characterizing the president's speech as the start of a long dialogue, White House officials acknowledged in interviews that they faced a tough road ahead if they expected to change the minds of lawmakers who view the president's proposals as amnesty.

Tony Snow, the White House spokesman, said during a briefing that amnesty was what President Ronald Reagan backed in 1986 in supporting legal status for nearly three million illegal immigrants, not what Mr. Bush was proposing now.

White House officials said Mr. Cheney, who has deep ties to House Republicans and remains influential among conservatives, would begin to play a larger role in the debate.

In his interview with the vice president, Mr. Limbaugh highlighted studies asserting that guest worker provisions would expand the number of foreign-born citizens by tens of millions.

"Well, if that's the case," Mr. Cheney said, "I would hope that would inform the debate and that Congress will consider those kinds of impacts very carefully before they finally pass something. We'll certainly weigh in on it."