After months of partisan rancor over the record federal debt and spending cuts to reduce it, congressional Republicans are working to avoid the heated political warfare when Congress turns its attention to annual spending measures next month.

Even as a new bipartisan committee begins work on a difficult and potentially contentious strategy to reduce federal spending by more than a trillion dollars over the next decade, leaders of both parties have expressed optimism that there will be minimal acrimony as they work to complete a series of 12 spending bills to fund the work of federal agencies for the next fiscal year, which begins Oct. 1.

Such an agreement would lift the threat of a government shutdown that has loomed over the budget and debt clashes of most of the year, providing some relief for federal workers who have faced the possibility of involuntary furloughs in recent months.

Despite the optimism, recent history suggests there could be trouble. It is not yet clear if rank-and-file members, many of whom were elected in 2010 promising never to back down from an opportunity to cut spending, will sign on.

The repeated clashes between the new GOP majority in the House and Democrats, who control the Senate and the White House, brought the government to the brink of a shutdown in April and close to financial default in August. For legislators whose public reputations have been bruised by the protracted sense of crisis, it may be a chance to show that Congress still knows how to complete its its day-to-day business.

The appropriations measures, the most crucial work Congress must get done each year, have been stalled for months over disagreement between the parties over a total amount of spending for the the year.

But in recent weeks, House Majority Leader Eric Cantor (R-Va.), Appropriations Chairman Harold Rogers (R-Ky.) and Senate Minority Leader Mitch McConnell (R-Ky.) have each indicated that Congress should accept the $1.043 trillion funding limit set in the recent deal to raise the nation’s legal borrowing limit, and have been urging that topline number on their GOP colleagues.

Right after the debt deal was completed, McConnell praised it for allowing Congress to return to a “normal appropriations process.” He noted the deal included agreements for overall spending levels not just for 2012, but also for fiscal year 2013.

“It’s my hope, and I know it’s the majority leader’s hope, that we will be able to do the basic work of government, which is the Appropriations Committee reporting bills, moving them across the floor of the Senate, and getting them done,” McConnell said.

Those statements are key because while the debt deal requires a $21 billion cut in spending for the coming fiscal year — the first step of $917 billion in cuts over the next decade negotiated in the deal — the Republican-led House had been on a path to slash even more.

The House already had approved six spending bills using the budget framework devised by Rep. Paul Ryan (R-Wis.), which included deeper spending cuts for the year.

Some conservatives, already dissatisfied by the debt deal, are likely to insist that the debt deal sets an upper limit for spending — and the GOP should fight to cut more.

In a memo to House members last week, Cantor attempted to defuse such voices. He wrote that accepting the limits is one of several moves Congress could make to help remove uncertainty from the economy.

“While all of us would like to have seen a lower discretionary appropriations ceiling for the upcoming fiscal year, the debt limit agreement did set a level of spending that is a real cut from the current year level,” he wrote. “I believe it is in our interest to enact into law full-year appropriations bills at this new lower level.”

Rogers last week called the spending level included in the debt deal a “responsible” amount that will save billions. He said he is committed to abiding by it.

“It is imperative that the Congress complete these must-pass bills in a timely manner to avoid the harmful, destabilizing effects caused by a delayed and drawn out Appropriations process,” he said.

The process has become so bogged down in recent years that there is little expectation that Congress can complete work on the bills by the time the new fiscal year begins Oct. 1.

But there is bipartisan optimism for swift agreement on a continuing resolution that will fund the government for a few weeks or months, followed by a broader agreement over how to divvy up funding for the 2012 fiscal year, perhaps by the end December.

The Senate has more work ahead of it than the House — it has passed only one of 12 separate spending bills, laying out appropriations for military construction and veterans affairs.

Leaders hope the debt deal will provide a framework to start. Beyond providing agreement on overall spending, it also provides guidance on how to prioritize spending, requiring that $684 billion spent be spent on security areas, including defense, and $359 billion be spent on non-security areas.

“Going through what we’ve gone through, everyone has realized there’s little benefit to a protracted, contentious fight like we’ve had all through this year,” said a House GOP aide.

But some freshmen member have continued to tout the Ryan budget, with its deeper spending cuts for the coming year, during meetings with constituents during the August recess — and they may not be anxious to adopt the debt deal’s higher spending levels.

“I think we should be looking for more,” said Rep. Kevin Yoder (R-Kan.), who is a member of the Appropriations Committee who voted against the debt deal. “The level set by the recent debt ceiling bill is really a ceiling. Congress has full authority to spend less than those levels.”

Leaders are hoping they will be able to quickly move the bills by relying on the same bipartisan votes that approved the debt deal.

But they will likely take heat from the 66 Republicans who opposed the deal on the grounds that it cut too little and the 95 Democrats who voted against it because they believed it cut too much.

And the two sides could also clash over issues other than spending — policy riders attached to the measures, including proposals to scale back the Democrats’ health care law and restrain the Environmental Protection Agency.

For hundreds of thousands of federal employees, a smooth appropriations process would mean not having to worry about a shutdown in coming months.

But the the deep cuts agreed to in the debt deal means workers will not exactly be breathing easily, said John Gage, president of the American Federation of Government Employees, which represents 600,000 employees of 44 federal agencies.

“It’d be good if some agreement could be made,” he said. “But I don’t’ think you’ll see federal employees dancing in the streets.”