With President Barack Obama signing into law the $2.1 trillion debt deal Tuesday, the nation averted a historic default and might have cleared the way for a more productive Congress.

The larger sense in both parties was one of relief after the bruising partisan slugfest on the debt ceiling that had brought the nation’s other business to a virtual standstill.

While Congress wrestled with the debt ceiling, plenty of other issues languished — including energy, education reform, consideration of the war in Libya, trade deals and more — to the chagrin of rank-and-file lawmakers who spent much of the past few months waiting for a handful of leaders to hash out a deal.

“We have avoided default, but the drawn-out process has distracted us from other important issues, including ongoing military engagements, competitiveness in the global economy and job creation here at home,” Sen. Jim Webb (D-Va.) said. “It is time to start focusing on our true strategic interests.”

The battle brought the nation to the brink of an economic catastrophe and took a toll on the poll ratings of Congress and the president alike; all sides seemed eager to pivot to something else after the measure cleared its final hurdles Tuesday.

Most lawmakers declared their interest in focusing on jobs — and they will have three months to work on regular business before having to consider the recommendations of a powerful new joint committee tasked with finding at least $1.2 trillion in additional deficit reduction as part of the debt deal.

The deal also effectively gave Congress a budget for spending bills for the next two years, a scenario that could smooth the way for Congress to avoid more brinksmanship over a government shutdown before the 2012 elections, Senators said.

Ultimately, the debt package passed both chambers with large bipartisan margins that belied the drama that marked the past few months, with negotiations blowing up again and again primarily over the issue of taxes. The Senate voted 74-26 on Tuesday to clear the bill after the House passed the measure Monday, 269-161. Leaders in both parties called the deal a triumph of compromise, but it was clear Tuesday that the biggest battles had simply been punted a few months down the road.

Though Obama relented to a deal with Republicans without any upfront revenues, the president said Tuesday that he is still looking for the “balanced approach” that he had originally sought. He said the new Joint Committee on Deficit Reduction created by the law should institute changes to entitlements, such as Medicare, and also to the tax code.

“I’ve said it before; I will say it again: We can’t balance the budget on the backs of the very people who have borne the biggest brunt of this recession,” Obama said. “We can’t make it tougher for young people to go to college or ask seniors to pay more for health care or ask scientists to give up on promising medical research because we couldn’t close a tax shelter for the most fortunate among us. Everyone is going to have to chip in. It’s only fair. That’s the principle I’ll be fighting for during the next phase of this process.”

Many Republicans chalked up the deficit reduction deal as an opening victory in their quest for smaller government, and it came despite having a Democrat in the White House and a Democratic majority in the Senate.

Senate Minority Leader Mitch McConnell, who played a key role in brokering the deal and received a cheer from the GOP Conference in its weekly lunch, said that far from showing dysfunction, it was a debate that “Washington very much needed to have.”

The Kentucky lawmaker said the debate will be a template for all future debt limit increases.

“Never again will any president be allowed to raise the debt ceiling without being held accountable for it by the American people,” he said.

Democrats grudgingly accepted the plan, which significantly limits spending for the domestic programs that they have championed, in return for avoiding a potentially catastrophic crisis.

“Our country was literally on the verge of a disaster,” Senate Majority Leader Harry Reid said.

The Nevada Democrat hailed the bill as a compromise that would help reduce the deficit and stabilize the economy. Reid warned that the Joint Committee on Deficit Reduction cannot simply include spending cuts without addressing revenue.

“That’s not going to happen; otherwise, the trigger is going to kick in,” he said. Under that trigger, defense and domestic programs including Medicare would face an automatic $1.2 trillion spending cut starting Jan. 1, 2013 — the same date the Bush tax cuts are slated to expire.

For some liberals, the bill was too bitter a pill. Sen. Jeff Merkley (Ore.) said Republicans used “extortion” to get Democrats to agree to the plan.

Conservative Republicans complained the package left almost all of the cuts to 2013 and beyond — effectively leaving it up to the next Congress and the president. More than 98 percent of the claimed savings would come after next year’s elections.

Sen. Jerry Moran said the deal merely reduces projected increases in spending over the next decade. And the $21 billion in deficit reduction over the first year of the agreement would cover less than a week’s worth of borrowing, the Kansas Republican noted.

Republicans and Democrats alike also complained about the two-step nature of the deal, with a $917 billion agreement to slice spending over the next decade now and an additional $1.2 trillion to $1.5 trillion to come later from the new joint committee by Thanksgiving.

“We’ve wasted this crisis,” Sen. Tom Carper (D-Del.) said on the floor Monday, adding that the Senate should have embraced the $3.7 trillion “gang of six” plan that was based on the Bowles-Simpson plan from last year’s fiscal commission.

Minority Whip Jon Kyl (R-Ariz.) supported the deal, although he said the defense cuts, including the spending cut trigger, came close to a violation of lawmakers’ oath of office.

Of the 74 Senate supporters of the bill, 46 were Members of the Democratic Conference and 28 were Republicans. Six Democrats, 19 Republicans and Democratic-leaning Independent Sen. Bernie Sanders (Vt.) voted against the deal.