While provisions to raise the debt limit and create a Congressional deficit reduction committee drew most of the attention in the legislation that allowed the government to narrowly avert a default, House and Senate leaders also used the measure to establish federal spending limits for the next two years.

Lawmakers are still likely to clash over just how the money is parceled out to various agencies and the Pentagon. But members of both parties say the bipartisan compromise on overall spending makes it unlikely that an impasse will push Congress back to the brink of closing the government in a repeat of the April showdown that ended just hours before federal money ran out. The current fiscal year ends Sept. 30.

“It substantially reduces the risk of a shutdown fight,” said Representative Chris Van Hollen of Maryland, the senior Democrat on the Budget Committee, who added that the prospect of spending certainty helped him sell the debt limit agreement to his fellow Democrats.

In the debt limit bill, Congress allotted $1.043 trillion for spending on federal agencies and national security in 2012, an amount that does not include money for so-called mandatory programs like Medicare.

That level is $7 billion less than current spending, but $24 billion more than would be allowed under the budget drafted by Representative Paul D. Ryan, Republican of Wisconsin, and passed by House Republicans earlier this year. The ceiling rises to $1.047 trillion in the 2013 fiscal year, potentially saving Congress from another politically charged spending fight before the midterm elections in November 2012.

With the Congressional appropriations process in a shambles in recent years and the government running for months at a time on stopgap bills, leaders of both parties say the agreement could restore some order.

“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,” said Representative Harold Rogers, Republican of Kentucky and chairman of the House Appropriations Committee.

Still, obstacles remain. Congress has not passed even one of the 12 spending bills due by Oct. 1. While the new agreement is expected to accelerate consideration of spending measures, the shortage of time means the House and the Senate will probably have to again enact temporary stopgap measures to give lawmakers a chance to assemble the bills and bring them to the floor.

At the same time, some conservative activists are pressing House Republicans to insist on lower overall spending totals, noting that the debt limit legislation established ceilings but does not require that all the money be spent.

In an internal survey released last week, the conservative House Republican Study Committee asked its members to weigh in with their views on the new spending levels and how conservatives can use the coming spending deadline as leverage to continue to push for cuts.

But Mr. Rogers and House Republican leaders like Representative Eric Cantor of Virginia, the majority leader, are advocating that Republicans abide by the new agreement and not try to force lower spending.

“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,” Mr. Cantor said in a recent memorandum to his colleagues. “I believe it is in our interest to enact into law full-year appropriations bills at this new lower level.”

The Republican leadership would also like to focus most of its firepower on the new deficit reduction committee created under the debt limit deal and its efforts to find $1.2 trillion or more in savings over the next decade — a process with the potential for a bigger budgetary impact than another protracted tussle over just a few billion dollars in annual spending. The spending fights are taking a definite toll on the public’s view of Congress, according to recent polls.

Mr. Van Hollen and other Democrats noted that a push for cuts below the newly established levels would make Republicans look as though they were reneging, since the leadership negotiated the spending agreement and it was backed by most House Republicans as part of the legislation to break the debt limit impasse.

Even with the agreement on the so-called top-line dollar figure, Democrats and some Republicans say the spending restraints will force difficult choices since real spending would be reduced for agencies that have already absorbed a first round of cuts in the spending deal struck last April.

Aides have already begun trying to identify programs that can be trimmed back, and they predict that the House and Senate will face tough negotiations over spending on individual programs.

Efforts to add contentious policy provisions to the spending measures are also expected to set off partisan disputes. House Republicans have shown a determination to try to use the spending measures to block implementation of the new health care law, limit regulatory efforts by the Environmental Protection Agency and other agencies, and impose other restrictions on the Obama administration. While those fights could be messy, top lawmakers and aides do no expect them to prompt a government shutdown.

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