Rep. Tom Price, R-Ga., calls it the "$64,000 question," and then promptly answers it.
"People will be supportive of almost any decreases in spending as long as they believe they're done in an open, equitable and fair manner," said Price, a member of the party leadership.
Democrats, already eyeing the 2012 elections, sound disbelieving.
"I'm not sure which country they're speaking to," said Rep. Debbie Wasserman Schultz, D-Fla. "How they think that slashing dramatically slashing important programs is going to help jump start the economy is beyond me."
The polls make clear the potential risks for both sides.
In an Associated Press-CNBC survey last November, shortly after Republicans scored large gains in the midterm elections, 87 percent of those polled said record federal deficits were likely to cause a major economic crisis over the next decade. Also, 85 percent said the cost of financing the federal debt would cause problems for their children or grandchildren.
Yet only 47 percent said cutting spending should be a higher priority than increasing it on education, health care and alternative energy development, which was backed by 46 percent.
In a CNN survey last month, those questioned said by an 81-18 margin that is was more important to prevent significant cuts to Medicare than to reduce the deficit. For Social Security, the split was 78-21.
So far, the House has been awash in Republican rhetoric about spending cuts. But with Congress still getting organized for the year, relatively little actual chopping has occurred.
The House voted to reduce its own budget, went on record in favor of eliminating federal subsidies for presidential candidates and party conventions, and cheered itself for setting goals for cuts.
This changes in the coming week, when work begins on a bill to keep the government in operation after March 4, but at a level $35 billion lower than enacted for last year.
"These cuts will not be easy, they will be broad and deep, they will affect every congressional district, but they are necessary and long overdue," Rep. Hal Rogers of Kentucky, the House Appropriations Committee chairman, said in a statement.
The cuts will be specific and on a large scale, for the first time, as Republicans tackle a federal deficit projected to reach $1.5 trillion this year, and an accumulated debt of more than $13 trillion.
Whatever the longer-term ramifications, Republicans who were sworn into Congress for the first time last month are eager to begin.
"I think people, even in government in my local communities, are saying, 'Yeah, we get it. We understand. We have to do something," said Rep. Sean Duffy, elected to a seat in Wisconsin long held by Democrat David Obey, who was chairman of the committee with jurisdiction over spending on domestic programs.
"I don't feel there's a backlash even in the district that had the benefit of David Obey's earmarks," Duffy said.
Added Rep. Jeb Hensarling of Texas, in the Republican's weekly radio and Internet address: "In order to get Americans back to work and create jobs, there is no limit to the amount of spending that we're going to be willing to cut."
Already, it is evident that dozens of new Republicans, many backed by tea party supporters, want more, not less, when it comes to spending cuts.
When the leadership directed that Rogers slice $35 billion, some conservatives said they want more.
"I think you're going to see it get below that" by the time the House sends the measure to the Senate, Duffy predicted.
Last fall's GOP Pledge to America cited a goal of $100 billion for the year, and even though the fiscal year is more than half over, that's what many of the conservatives want as a strong first step.
If that's what the newcomers want, that's probably what they will get, because when added to the ranks of conservatives who were elected previously, they command a majority of the House.
Speaker John Boehner, R-Ohio, has pledged to give individual lawmakers ample opportunity to seek changes during floor debate.
Duffy and others have signed onto a proposal by the 175-member Republican Study Committee to eliminate dozens of programs as part of an attempt to reduce deficits by $2.5 trillion over a decade.
Not all of that would come in the first bill to reach the floor.
But no opportunity to press President Barack Obama and the Democrats will be overlooked. It's likely that several short-term bills will be needed while negotiations play out on the measure to tide the government over to September. The new budget year begins Oct. 1.
Republicans will want to ratchet down spending on each one, although Duffy and others say they want no part of a government shutdown.
Shutdowns summon painful memories for an earlier generation of Republicans. When Speaker Newt Gingrich led the rank and file into one in 1995, President Bill Clinton used it to depict him and them as irresponsible radicals.
Additionally, the Treasury Department has said Congress will need to raise its borrowing authority this spring. Boehner and other Republicans have said they will use that as leverage to force a series of changes in government spending habits.
Republicans also will release a budget this spring that is likely to call for changes in benefit programs such as Social Security and Medicare as well as other programs.
Over the summer and fall, they will send the Senate a series of spending bills for the 2012 budget year.
There will be plenty of opportunity to clash with Obama and try and reinforce Senate Republican leader Mitch McConnell's hand in negotiations with majority Democrats in the Senate.
"There are 87 new freshmen on our side of the aisle who came here to save the country," said Price.
EDITOR'S NOTE - David Espo is AP's chief congressional correspondent.