The market turmoil following last week’s debt deal — including Monday’s 600-point plunge in the Dow Jones Industrial Average — appears to have merely amped up partisan attacks.

Standard & Poor’s blamed, in large part, partisan gridlock for its historic downgrade of U.S. credit rating to AA+ from AAA Friday evening. But rather than causing the parties to look for ways to bridge their differences, their political arms went on the attack.

The Republican National Committee ripped President Barack Obama as the “not-so-AAA president” Tuesday morning and urged him to fire Treasury Secretary Timothy Geithner, while the National Republican Congressional Committee blamed Obama for resisting a balanced budget amendment to the Constitution.

Obama cast blame on the GOP’s months of debt brinkmanship in a speech Monday amid the stock market plunge.

“We knew from the outset that a prolonged debate over the debt ceiling — a debate where the threat of default was used as a bargaining chip — could do enormous damage to our economy and the world’s,” he said.

Obama said he would offer up his own proposals for the new Joint Committee on Deficit Reduction tasked with finding at least $1.2 trillion in deficit reduction over the next decade.

But in a campaign event Monday evening, the president didn’t sound too hopeful that his ideas would get enacted. He criticized Republicans for being dug into their “ideological purity” on tax revenue and started pointing to the next election as a chance for voters to weigh in.

“The challenge is simply that the politics in this town doesn’t seem to be equipped to make modestly tough choices,” Obama said at a fundraiser. “The good news is that I think there has been enough frustration at Washington — it sort of reached a fever pitch last week — that we’re now looking at 16 months in which there’s going to be a clear contrast and a clear choice to be made.”

House Majority Leader Eric Cantor, meanwhile, criticized the S&P in a Monday memo for citing Republican opposition to revenue as one of the reasons for the downgrade.

As a result of the downgrade, “There will be pressure to compromise on tax increases,” the Virginia Republican wrote. “We will be told that there is no other way forward. I respectfully disagree.”

Cantor said Republicans should “demand” the new joint committee focus exclusively on spending cuts.

Cantor also predicted fundamental reform of entitlements will have to wait until after the 2012 elections, and cited Budget Chairman Paul Ryan’s (R-Wis.) comments on Fox News Sunday lowering expectations for the joint committee.

Speaker John Boehner also reiterated his opposition to tax hikes.

“Just as both parties contributed to our unsustainable debt, both parties must work now to cut spending,” the Ohio Republican said.

The S&P downgrade had Democrats fuming. Senate Banking Chairman Tim Johnson (D-S.D.) noted that U.S. debt rallied strongly Monday even as the stock market dropped, showing that investors do not doubt they will be repaid.

“This irresponsible move by S&P may, however, have spillover effects that tax the American people by increasing interest rates on home loans, credit cards and car loans, and by increasing the cost of finance for some state and local governments,” Johnson said. “I am deeply disappointed in S&P’s decision to enter into the game of political punditry.”

Outside advocates for a large deficit reduction package tried to use the downgrade as a spur for compromise that would include big entitlement changes and new tax revenue.

Former Senate Budget Chairman Pete Domenici (R-N.M.) and former White House Office of Management and Budget Director Alice Rivlin, co-chairmen of the Bipartisan Policy Center’s Debt Reduction Task Force, sent a letter to leaders of both parties urging them to deal with both revenue and entitlements, as well as pass a large upfront payroll tax cut to spur the economy through the new joint committee.

“This committee has a historic opportunity to come to a broad bipartisan solution that will control debt and ensure America’s future prosperity,” they wrote.