WASHINGTON – Two top Republicans said Sunday that they oppose raising the nation’s debt ceiling without major cuts in the federal budget deficit, suggesting that the GOP may be heading toward a showdown with Democrats as the deadline for congressional action nears.

Senate Republican leader Mitch McConnell, R-Ky. said on NBC’s “Meet the Press” that he is prepared to keep the ceiling in place “unless we do something really significant about debt and deficit.”

Former Minnesota Gov. Tim Pawlenty, a Republican candidate for president, challenged the Obama administration’s contention that not raising the debt limit would trigger a default.

The U.S. has until Aug. 2 to raise the $14.3 trillion debt ceiling, according to Treasury Secretary Timothy F. Geithner. Failing to act would invite “catastrophic” consequences, Geithner has said. Military service members would not be paid, retirement investments would drop in value, and people would face higher payments on mortgages and car loans, he said.

President Obama has said he expects Congress to increase the ceiling. In an interview last month with The Associated Press, the president said: “We will raise the debt limit. We always have. We will do it again.”

The alternative, Obama said, is to “plunge the world economy back into a recession.”

Posturing is always a part of congressional negotiations, but Republicans are under enormous pressure from tea-party conservatives to curtail spending. The debt-ceiling debate presents some congressional Republicans with an unhappy choice. A vote to raise the ceiling might expose them to primary challenges in the 2012 election, while a vote against it risks a default on U.S. debt obligations that could jeopardize the fragile economic recovery.

Pawlenty, in an interview on ABC’s “This Week,” asserted that the consequences of failing to raise the cap might not be as dire as the White House says.

Asked whether the result would be calamitous for the U.S. economy, Pawlenty said: “Well, there are some serious voices challenging that very premise. And the answer is nobody really knows, because we’ve not been at this point before.”

Obama has said he is amenable to additional spending cuts as a condition of lifting the debt ceiling.

In the end, the markets could bridge the divide.

Peter R. Orszag, Obama’s former budget director, predicted in a speech last week that the impasse may soon cause bond market fluctuations that demonstrate the real cost of inaction.

“We are going to deal with the problem when we have significant external pressure to do so,” said Orszag, who is now vice chairman for global banking at Citigroup.