The parties appear to be moving on parallel tracks as the nation draws nearer to a possible default after Aug. 2, unless Congress can find a way to agree to increase the nation's debt limit, which now stands at $14.3 trillion.
Boehner wants a two-tiered approach in which Congress would cut $1.2 trillion in spending in exchange for a debt limit increase that would allow the government to pay its bills through the end of the year. The plan includes another increase in the debt limit and another round of spending cuts to cover all of 2012.
Senate Majority Leader Harry Reid and President Barack Obama favor a plan that would eventually cut $2.7 trillion in government spending, while increasing the debt limit by $2.4 trillion, which would keep the government going through the end of next year.
Chaffetz dismissed both approaches, saying that neither goes far enough to solve the debt problem. He predicted that Boehner's plan will fail on Wednesday unless Democrats unexpectedly support it.
"I don't believe they can get there with just Republicans," he said.
Chaffetz plans to join a block of House Republican freshmen, swept in during the tea party wave of 2010, who oppose the plan because it does not require the passage of a balanced budget amendment to the Constitution.
Boehner attempted to appease the right wing of his party by including a requirement that the House and Senate vote on such an amendment after Oct. 1. But it clearly hasn't worked.
"I don't see anyway I can support it," Chaffetz said. "I plan to stand tall on principle. Too many in the past have caved. That is why we are in this mess."
Bishop said he also wants a balanced budget amendment, but he's not ready to say that he would oppose any debt limit deal that doesn't require one. He said he sees benefits in Boehner's two-tiered approach, which would require Congress to accept $1.8 trillion in cuts identified by a bipartisan super committee before the debt limit could rise enough to cover the expected needs of 2012.
"Instinctively, I'm not opposed to taking a down payment and then moving forward," said Bishop, who wants to read the bill before deciding how he will vote.
Matheson was hoping for a larger bipartisan deal like the one Obama and Boehner tried to reach last week. Since that effort collapsed, Matheson says he favors the Senate's longer-term approach over the House Republicans' two-tiered plan.
"More of a longer term solution is clearly better for everybody," Matheson said.
Utah's two senators Orrin Hatch and Mike Lee have previously joined Chaffetz in signing a pledge to vote against any increase in the debt limit until Congress passes a balanced budget amendment. They would, therefore, oppose both of the options now on the table.