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“Once the Senate announced their amnesty bill, Giuliani and McCain had the albatross of amnesty hung around their necks,” said Rep. Steve King, Iowa Republican. “I’ve said for months you can’t win the Iowa Caucus if you support amnesty.”

Iowa’s first-in-the-nation caucus “will punch at least two tickets to New Hampshire and they will be the most viable candidates for the Republican nomination for president,” Mr. King said.

In South Carolina, Mr. Graham faces re-election next year, but Republican officials there said he is unlikely to face a primary challenger. Still, Mr. Beltram said he advised Mr. Graham to distance himself from Mr. McCain’s presidential campaign, which Mr. Beltram says “is heading south” in his state.

The most recent poll in South Carolina, by the American Research Group, showed Mr. McCain with 32 percent to 23 percent for Mr. Giuliani among South Carolina Republicans.