WASHINGTON (AP) — House Republicans are embracing a step-by-step approach to immigration, in contrast to the sweeping plan passed by the Senate and backed by the White House. But they're offering neither specifics nor a timetable — nor any mention of possible citizenship for an estimated 11 million immigrants living in the country unlawfully.

Speaker John Boehner, R-Ohio, and other Republican leaders said in a statement the administration "cannot be trusted to deliver on its promises to secure the border and enforce laws as part of a single, massive bill like the one passed by the Senate."

House GOP lawmakers streaming out of a two-hour meeting on immigration Wednesday also shrugged off a long-distance nudge from former President George W. Bush, who called on Congress to reach a "positive resolution" on the issue.

"America can be a lawful society and a welcoming society at the same time," Bush said at a naturalization ceremony at his presidential library in Dallas.

"We care what people back home say, not what some former president says," declared Rep. Tim Huelskamp, R-Kan.

President Barack Obama is to meet Thursday with two authors of the Senate measure, John McCain, R-Ariz., and Chuck Schumer, D-N.Y., in the Oval Office.

The Republican meeting in the Capitol was arranged as a listening session for the House GOP, their first such session since the Senate approved far-reaching legislation last month on a bipartisan vote of 68-32.

Lawmakers said afterward there was support for a bill to create a path to citizenship for immigrants who were brought to the country as children illegally by family members, an idea advanced by Majority Leader Eric Cantor of Virginia.

Several members of the rank and file said Rep. Paul Ryan, R-Wis., had made a particularly strong appeal for a comprehensive approach, which includes possible citizenship for the 11 million.

But others emphasized there was virtually no support for the Senate's approach of one sweeping measure that dealt with immigration in all its forms.

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And there is no clear timetable.

"I don't sense any urgency," said Rep. John Fleming of Louisiana. Rep. Peter King of New York said that if any legislation came to the floor for a vote this month, it would deal only with border security.

Other lawmakers said even that approach raised concerns. Dealing with border security, they said, could lead to negotiations with the Senate that could morph into a compromise granting citizenship for some of the immigrants in the country illegally. They sought and received assurances from Boehner that he wouldn't let that happen, according to Rep. Kevin Cramer of North Dakota.

Boehner had said he wants the House to pass legislation on the subject before lawmakers go home for a four-week break over August, beginning with a measure to toughen border security. He has also said he won't put any bill on the House floor that doesn't have the support of at least half of the GOP rank and file, a pledge that only increases the challenge for Democrats and others who want to give a chance at citizenship to millions now in the country illegally.

In explaining their piecemeal approach, Boehner and fellow GOP leaders said the administration's recent decision to postpone a key element of the health care law shows it can't be trusted to carry through on commitments, such as the one in the Senate immigration bill requiring the borders to be secured before a path to citizenship is opened.

Unlike the comprehensive, bipartisan bill that cleared the Senate last month, the House Judiciary Committee has cleared four smaller measures in recent weeks, none of which would include the possibility of citizenship.

One would toughen enforcement of immigration laws and includes a provision that would permit local police officers to enforce such laws as part of an attempt to raise the number of deportations.

Other measures would create a new mandatory system for employees to verify the legal status of their workers, create a new temporary program for farm workers and expand the number of visas for employees in technology industries.

By contrast, the Senate bill would increase border security, provide a pathway to citizenship for many of the estimated 11 million immigrants illegally in the country, expand the highly skilled worker program and set up new guest worker arrangements for lower-skilled workers and farm laborers.

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Associated Press writers Henry C. Jackson, Donna Cassata, Alan Fram, Chuck Babington and Ken Thomas in Washington and Jamie Stengle in Dallas contributed to this report.