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Republicans have demonstrated that they have enough votes to sustain a veto on spending bills and will work with the president on the issue. Rep. Jeb Hensarling, Texas Republican, said 147 House Republicans — one more than necessary — have signed a pledge to uphold Mr. Bush’s vetoes on the nine spending bills.

The House Republican leadership delivered the pledge letter to Mr. Bush on Wednesday at the White House, during a meeting about the spending showdown with Democrats.

Mr. Hensarling acknowledged that many House conservatives would oppose the Senate immigration bill, but that immigration may not come up for debate in the House until late next month or early August.

“Right now we are certainly united with the president in trying to get these over-budget, bloated spending bills vetoed,” he said. “There are so many fights here, you’ve got to focus on the one in front of you and not the one down the road.”