Washington (CNN) - Republican opposition is growing over the continuing resolution that would fund the government for three additional weeks.
Both parties agreed last week to move ahead with a three-week stopgap bill that would cut an additional $6 billion from current spending levels, avoiding a potential federal shutdown when the current continuing resolution expires Friday. The House will vote Tuesday on the new agreement, but some Republicans argue the cuts don't go far enough.
Republican Rep. Jim Jordan of Ohio, who serves as chairman of a key bloc of House conservatives, said he will vote against the three-week spending plan when it comes before the chamber for a vote.
"Americans sent us here to deal with big problems in bold ways. We're borrowing billions of dollars a day, yet Senate Democrats have done little more than wring their hands for the last month," Jordan said in a statement. "Democrats control both the Senate and the White House, and it's time they stopped dithering. We need swift action to deal with spending for the rest of this year."
Republican Rep. Tom Graves of Georgia, a freshman member of the House Appropriations Committee, said President Obama and leading Democrats in the Senate are "failing to fully engage in this debate," compared to House Republicans who, he said, have "done their job."
"Let's close the book on 2011 funding with common sense debt reduction and then move on to the critical tasks of making government more efficient, enacting long-term spending reforms, and modernizing entitlements," Graves said in a statement.
The legislation under consideration this week was drafted by the Appropriations Committee, making Graves' announcement more unusual.
President Obama and Congressional leaders all say they want to avoid a government shutdown, but the parties remain at odds over how to address the immediate need to authorize government spending for the next six months and the long-term need for budget reforms that reduce the deficit and national debt.
Last week, the Senate rejected the House bill, as well as an alternate proposal from Senate Democrats that would cut $6.5 billion from the current spending levels for the rest of the fiscal year, which ends September 30.
At a meeting with reporters Monday, House Majority Leader Eric Cantor said "there is a lot of frustration" that Congress has been unable to pass a spending bill for the rest of the year.
"Obviously there are a lot of other issues that we would like to see dealt with in any kind of longer term solution," Cantor said. "But right now we are trying to position ourselves so that we can ensure there is not a government shutdown, but to continue cutting spending and reach a result that I think that we can get a majority of members to go along with."
Republican Rep. Jeff Flake of Arizona was another member of Congress to come out against the deal.
"How are we ever supposed to tackle the grave fiscal challenges before us like the debt ceiling, the debt, and the FY2012 budget when we just keep punting on FY2011 spending?" Flake said in a statement.
And on the Senate side of Capitol Hill, Marco Rubio said he, too, would oppose any additional short-term solutions.
"While attempts at new spending reductions are commendable, we simply can no longer afford to nickel-and-dime our way out of the dangerous debt America has amassed,” Rubio said in a statement. “It is time our leaders in Washington wake up and realize that we are headed for a debt disaster."
The freshman senator said the country can avoid a government shutdown if the president "steps up to lead and if politicians from both parties finally get their act together."
- CNN's Deirdre Walsh and Tom Cohen contributed to this report