Rep. Mike Pence, R-Ind., said there is a need for dramatic spending cuts in "big-ticket items."
However, Democrats appearing on Sunday news programs questioned how President Bush can trim the budget to pay for Katrina recovery and support tax cuts for the wealthy.
"Where is he going to find roughly half a trillion dollars over the next several years for Iraq and for Katrina?" Sen. Joseph Biden, D-Del., on television news. "I think we're not leveling with the American people."
Raising taxes or not making permanent the president's tax cuts is not the answer now, said Pence, head of the Republican Study Group, the spearhead group for the GOP's most conservative members.
"We simply cannot break the bank of the federal budget," Pence told ABC.
"We simply can't allow a catastrophe of nature to become a catastrophe of debt for our children and grandchildren," he said.
The drug benefit program, set to begin Jan. 1, is expected to cost $40 billion a year. Last month President Bush signed a $286.4 billion highway bill that has been criticized for including about 6,000 projects added by lawmakers to benefit their districts and states.
Setting aside all of those additional highway projects and delaying the drug benefit by a year are expected to be among the proposals House Republicans are preparing for "Operation Offset" this week, Pence said.
"We need to rebuild," he said. "We can find the cuts in Washington, D.C., to do that, I really believe that."
Sen. David Vitter, R-La., said tax increases will not be a part of the recovery plan he intends to offer this week. Although cuts in spending and delays in spending already approved will not be in his proposal, Vitter said he is open to considering such actions.
Vitter said people should not take on faith that Republicans will make cuts in light of the high spending during the Bush administration.
"We haven't been disciplined enough over the last 10 years. We need to do that, and we needed to do that before Katrina. We still need to do that over the medium and long term," Vitter said.