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“I think the Republican leadership and the Democratic leadership have all come to the conclusion that it’s more likely the president would win out in that scenario, because they seem to be informed by the single experience in 1995. Therefore, I think the Democrats wanted to initiate a shutdown because they have a Democratic president who would win this,” said Rep. Steve King, Iowa Republican, a tea party favorite who says his chief goal is to defund the health care law.

Mr. King said he is making his case to Republican leaders, but said they are “not yet” open to the idea of a shutdown.

“There is a coming confrontation between the House majority and Barack Obama,” Mr. King said. “If Republicans should decide that we’re going to avoid a shutdown, the net result will be the president of the United States will get everything he’s willing to fight for.”

Caught in the crossfire from tea partyers and Democrats is Mr. Boehner.

While still negotiating with Democrats, he has intensified his criticism of them, arguing that the House has already passed a bill, while the Senate has not.

“Now the Senate says: ‘We have a plan.’ Well, great — pass the damn thing, all right? And send it over here, and let’s have real negotiations, instead of sitting over there and rooting for a government shutdown,” he said.

The tussle over the current year’s spending is likely to spill into broader fights over the budget for 2012, and whether to raise the national debt limit — two debates that are expected to kick off early next month and are likely to be front and center at Thursday’s rally.