As they tried to blame President Obama for the nation’s lowered credit rating, the Republican presidential candidates who squared off Thursday night in Iowa made several misleading, incomplete or simply false claims.

“I was fortunate enough to be a governor that got an increase in the credit rating of my state at the same time we got a president who got a decrease in the credit rating of our nation,” said Mitt Romney, the former governor of Massachusetts.

Representative Michele Bachmann of Minnesota repeated her assertion that “we should not have increased the debt ceiling” — which would have led the nation to default.

Mrs. Bachmann misrepresented the debt ceiling deal when she complained that Congress had given a “blank check” to President Obama by raising it. The debt limit had to be raised to pay for the bills that Congress had already approved, not future spending. And the final deal required reducing the deficit by some $2.1 trillion over the next decade.

Her gloss of the warning issued by Standard & Poor’s, the agency that lowered the nation’s rating, was off as well. “When they dropped our credit rating, what they said was we don’t have an ability to repay our debt,” she said.

That is not what it said. Standard & Poor’s has carefully avoided partisan finger-pointing in its comments. But some of the factors it cited — from the “political brinkmanship” that left the nation at the precipice of default to its concerns that the deficit-cutting deal “falls short” of what is needed — can be attributed to Republicans in Congress as much as, or even more than, President Obama.

The ratings agency lamented in its report on the downgrade that “the statutory debt ceiling and the threat of default have become political bargaining chips in the debate over fiscal policy.”

It was Republicans in Congress who made it a bargaining chip. They balked at raising the debt limit unless the White House agreed to a new package of spending cuts. The Obama administration initially sought a “clean” bill to raise the debt limit, but the Republicans prevailed.

When a bill to reduce the deficit and raise the debt ceiling was finally passed this month, the nation was just hours away from a default that economists warned would have harmed the fragile economy.

Of course, President Obama acted similarly to Mrs. Bachmann when he was in the Senate: he voted against raising the debt limit in 2006, a vote his aides say he regrets.

But prominent economists and business leaders have said a failure to raise the debt ceiling would have led to a default that would have hurt the economy. Ben S. Bernanke, the Federal Reserve chairman, testified that it would probably be “a recovery-ending event.”

Several Republicans assailed President Obama at the debate for not cutting spending enough. Standard & Poor’s warned that the final agreement “falls short of the amount that we believe is necessary.”

But President Obama pushed for a plan to cut the deficit by more — $4 trillion, with cuts to entitlement programs including Medicare and Medicaid, as well as some $1 trillion in new revenues. It was House Republicans who rejected it, opposing any tax increases and ultimately pushing for the smaller measure.

Mrs. Bachmann claimed that the deal had led to only “$21 billion in illusory cuts.” That was the amount projected for the very short term. The nonpartisan Congressional Budget Office found that the deal would cut the deficit by at least $2.1 trillion over the next decade.

Her complaint that the cuts were illusory also clashed with her own critique of the debt ceiling deal from last week, when The Des Moines Register quoted her as saying: “Under this debt-ceiling bill, do you know how this works? The first thing that gets whacked and with a hatchet is defense.”

Kitty Bennett contributed reporting.