WASHINGTON (AP) — The White House said Monday that a "significant" deal with Republicans on cutting government spending and raising the nation's debt limit is still possible, even as the administration hardened its stance on the need for increased tax revenue to be part of any agreement.

President Barack Obama made his first direct foray into the deficit negotiations Monday. He met with Senate Majority Leader Harry Reid in the Oval Office for about 30 minutes Monday morning, and planned to meet with Republican Sen. Mitch McConnell in the early evening.

White House spokesman Jay Carney said Obama's meeting with Reid was "constructive" and the president concluded that there are still opportunities for a deal to be reached. But he said the only way to achieve that objective would be to include tax increases or the elimination of tax breaks for big companies and wealthy individuals.

"It's the only way to get it done," Carney said.

The White House has proposed raising about $600 billion in new tax revenue, including ending subsidies to oil and gas companies, an idea that failed in the Senate.

The administration also would tax private equity or hedge fund managers at higher income tax rates instead of lower capital gains rates, change the depreciation formula on corporate jets and limit itemized deductions for wealthy taxpayers. It also has called for repealing a tax benefit for an inventory accounting practice used by many manufacturers.

But Republicans are demanding huge cuts in government spending and insisting there be no tax increases.

Ahead of his meeting with Obama, McConnell said Democrats' calls for tax increases do not amount to a "serious" position.

"It is my hope that the president will take those off the table today so that we can have a serious discussion about our country's economic future," McConnell wrote in an editorial that appeared Monday on CNN.com.

Absent an agreement that cuts long-term deficits, Republicans say they will not vote to increase the nation's borrowing, which will exceed its $14.3 trillion limit on Aug. 2. The administration has warned that if Congress does not raise the debt ceiling, it could mean the first U.S. financial default in history and send economic shockwaves around the world.

Carney wouldn't set a deadline for a deal Monday, saying he didn't want to name a "token timetable." He said Obama and Vice President Joe Biden would hold additional meetings with congressional lawmakers, though there were none scheduled at this point.

The president made his move to get personally involved in the negotiations on Friday, after bipartisan talks led by Biden stalled when Republican lawmakers abandoned the negotiations, saying the issues still on the table must now be addressed by the president.

Many economists and government analysts say the government needs to get control of its long-term debt by taming its deficits. The non-partisan Congressional Budget Office last week called the nation's budget outlook "daunting" and said that without major changes in policies, an aging population and rising health care costs would result in a surging federal debt.