WASHINGTON—President Barack Obama made the case Wednesday for ending certain tax breaks for "millionaires and billionaires" in a deal to keep the U.S. government from defaulting on its debt, sharpening his tone with just weeks left for Democrats and Republicans to reach an agreement.

Republicans responded by repeating their opposition to any tax increases, saying they would hurt the fragile economy.

Although the two sides appeared deadlocked, their differences are smaller than the partisan rhetoric suggests.

Senate Democratic leaders met with Mr. Obama Thursday for a briefing on the budget talks, and he told them he had made a general proposal to Republicans and hoped to get a response by the end of the week, according to a person familiar with the meeting. "There are negotiations involving the president and the leaders," said Senate Majority Whip Dick Durbin (D., Ill.), who was in the meeting. "He said he wants some time.''

Democrats and Republicans have agreed on about $1 trillion in spending cuts over at least 10 years. The final sticking point is whether to include some tax changes, as Democrats insist, or none, as Republicans want.

"You can't reduce the deficit to the levels that it needs to be reduced without having some revenues in the mix," Mr. Obama said during a news conference Wednesday. "The Republican leadership in Congress will, hopefully sooner rather than later, come to the conclusion that they need to make the right decisions for the country, that everybody else has been willing to move off their maximalist position and they need to do the same," Mr. Obama said.

Mr. Obama criticized Republicans for resisting Democratic calls for ending tax breaks for corporate-jet owners, hedge-fund managers and oil companies. Those proposals, which could raise as much as $64 billion over 10 years, would do little to dent the $1.5 trillion annual deficit, but would make it much easier for Mr. Obama to win Democratic support for a deal that likely will include deep spending cuts painful to his party.

President Obama, at a news conference Wednesday at the White House, took a sharper tone toward Republicans on debt-reduction talks. European Pressphoto Agency

Mr. Obama also suggested that some initiatives designed to stimulate the economy in the short term should be included in a final deal, singling out a yearlong extension of the payroll tax break for employees, which expires in January.

Republicans dismissed Mr. Obama's comments as just another Democratic call for economically damaging tax increases. "There's an important principle at stake in this debate. It's not about the rich versus the poor," Senate Minority Leader Mitch McConnell (R., Ky.) said in a speech Wednesday. "It's about whether Washington will ever be held accountable for its mistakes. That's why Republicans refuse to let the taxpayers take the hit when it comes to reducing the debt."

Negotiators are trying to find ways to get a deficit-reduction deal that can win enough Democratic and Republican votes to pass Congress, clearing the way for an increase in the $14.29 trillion federal borrowing limit. Treasury Department officials warn that the debt ceiling must be lifted before Aug. 2 or the government will run out of cash to pay all its bills, which could shake financial markets and cause another recession.

Moody's Investors Service Inc. said Wednesday that a U.S. debt default would lead not just to a downgrade of the government's top-notch credit rating, but also to lowering of other credit ratings linked to the government. These include ratings on bonds issued by mortgage-finance firms Fannie Mae and Freddie Mac, and bonds issued by banks guaranteed by the U.S. government.

President Obama speaks at a news conference addresses a more visible role in trying to settle a budget debate with Congress.

Until now, Republicans have largely set the boundaries of the debate. They demanded deep spending cuts in exchange for a vote to raise the debt ceiling, forcing Mr. Obama to propose a framework for a long-term, deficit-reduction plan. Mr. Obama has had to get more involved in the issue since bipartisan talks led by Vice President Joe Biden fell apart last week over an impasse on taxes.

On Wednesday, the president appeared to be responding to considerable frustration among members of his own party that Republicans have proven more effective in sticking to their principles. House and Senate Democratic leaders have told the president in private meetings over the last week that they would not accept a package that only included spending cuts.

Sen. Charles Schumer (D., N.Y.) remarked Wednesday that House Speaker John Boehner (R., Ohio) would have to accept tax changes to win the Democratic votes he will need to raise the debt limit. "He doesn't have the votes without revenues," Mr. Schumer said of Mr. Boehner.

Hitting the Ceiling See what the federal debt limit has been at year-end since 1940.

Mr. Boehner responded to Mr. Obama's comments in a written statement: "The president is sorely mistaken if he believes a bill to raise the debt ceiling and raise taxes would pass the House. The votes simply aren't there."

While Republicans control the House, some Democratic support will be needed to pass a debt-ceiling increase. And although Democrats control the Senate, they will need some Republicans to get the 60 votes needed to pass the measure.

GOP leaders on Wednesday also revived the drive to pass a constitutional amendment to require a balanced federal budget. House Republicans said they would hold a vote on such a measure in late July. Senate GOP leaders demanded a vote on a companion amendment.

The Senate version sets a cap on government spending at 18% of gross domestic product, requires a three-fifths majority in Congress to pass tax increases and includes other provisions designed to ensure that the budget is not balanced simply with higher taxes.

Mr. Obama put Congress on the spot in his remarks, suggesting that leaders work through the July 4 recess to get a deal. A group of Senate Republicans took up the offer Wednesday, pledging to block any recess.

Mr. Obama also stressed that Congress needs to raise the debt ceiling to cover the government's bills, not to accommodate additional spending. "The money's been spent," he said. "So this is urgent, and it needs to get settled."

—Damian Paletta

and Naftali Bendavid contributed to this article.