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Immigrant rights advocates say Republicans are increasingly isolated on the issue. They point to business groups, religious organizations and some social conservative advocacy groups that are demanding action.

Mr. Russo’s push adds at least some segment of the tea party movement to that group.

Steve Case, founder of AOL, who was part of the call with Mr. Russo, said enough Republicans have survived primary contests that their leadership can be confident in making tough decisions without voter backlash.

“Given the fact that the primary deadlines have largely closed, we do have a window here in the next two or three months. I think if we fail to get this done by the August recess we lose momentum,” Mr. Case said.

Sen. Jeff Sessions, an Alabama Republican who has led opposition to an immigration bill, said Americans should be worried about pressure on Congress from big businesses that are angling for more low-wage workers who, he said, will undercut their pay.

“It is not xenophobic but compassionate to say we should focus our attention on helping struggling American workers. It is not xenophobic but our patriotic duty to defend the integrity of our borders and the rule of law. It is the oath we all took as senators to defend the Constitution of the United States,” he said in a speech on the Senate floor.

Mr. Russo said the immigration issue won’t rate high in tea party endorsements. He said he expects groups to focus instead on core economic issues.

The Partnership for a New American Economy, which helped organize Mr. Russo’s announcement, said polling data showed that a majority of voters who sympathize with the tea party would be open to granting legal status to illegal immigrants, with strict conditions attached.

Still, the poll found those tea party voters place immigration last on a list of six issues that are critical to their votes for Congress this year. Government spending and debt remained at the top.