President Obama, facing a narrowing window in which to strike a debt reduction deal, was using shuttle diplomacy Monday as he tries to bridge the chasm between congressional Democrats and Republicans over tax hikes.

Meeting separately with the top party leaders in the Senate, the president and Vice President Biden are trying to salvage bipartisan talks that broke apart last week when GOP negotiators walked away after refusing to agree to tax hikes. Obama met Monday morning with Senate Democratic Leader Harry Reid, and plans to see Senate Republican Leader Mitch McConnell late Monday afternoon.

Republicans are demanding steep spending cuts as a condition for supporting an increase in the debt ceiling. They claim Democratic negotiators in the Biden-led talks have been pushing too hard for tax increases as part of that deal -- kicking it up to Obama and party leaders to figure out the next step.

White House Press Secretary Jay Carney, describing the meeting with Reid as constructive, said Democrats are willing to tackle the tough problems but called on Republicans to open discussion on their "sacred cows" -- a reference to tax hikes.

"We obviously believe a balanced approach is the right approach and we're not alone here. It's important to remember, there are a number proposals out there in this time period that have been made. The only one that doesn't take a balanced approach has been the House Republican proposal," Carney said.

What constitutes a tax hike, though, is a matter of debate. Republican leaders say that tax hikes, as a practical matter, cannot pass Congress and therefore should not be included in any deal.

"What we object to is changing the tax code. We don't need new taxes right now. We need to reduce spending," said Senate Minority Whip Jon Kyl, R-Ariz., who walked out of the Biden negotiations last week.

But House Minority Leader Nancy Pelosi said eliminating tax subsidies is not an increase in taxes.

"When it comes to these tax subsidies for big oil, for corporations sending jobs overseas or giving tax breaks to the wealthiest people in the country ... Closing special interests tax subsidies is what they have walked away from," she said.

House Assistant Minority Leader James Clyburn, D-S.C., agreed that ending a subsidy is not an increase in taxes.

"How do you call closing loopholes to oil companies that are making billions of dollars in profits, closing up these loopholes that would generate $40 to $50 billion in revenue, how do you call that a tax hike?" he said on ABC's "This Week." "That is no tax hike. You only hike taxes when you raise rates. We are not asking anybody to raise anybody's rates."

Rep. Chris Van Hollen, D-Md., ranking Democrat on the House Budget Committee, said Friday that Democrats were also looking at phasing out deductions for people making over $500,000 a year.

But with House Speaker John Boehner reiterating Friday that Republicans want tax hikes off the table, Kyl criticized the plan to close so-called "loopholes" a path to higher gas prices and punishment of a single industry.

"That kind of tax increase is going to flow right to the consumer. Everybody knows that," Kyl , told "Fox News Sunday."

Kyl said "tax expenditures" -- or subsidies -- are breaks given to companies that force the Treasury to forego taxes. He said any attempt to reduce them would have to be accompanied with plans to reduce the overall tax rate, and Congress doesn't have time for that as the debt limit talks push up against an Aug. 2 deadline to avoid a potential U.S. default.

Kyl also did not rule out raising revenue in the course of budget talks. He defined a tax hike as a change in the tax code, suggesting Republicans would be willing to find money outside the tax code.

"We have not refused any new revenue. For example, we've been discussing some fee increases and some other things that would actually generate revenue," he said. "But what we object to is changing the tax code. We don't need new taxes right now. We need to reduce spending."

Underscoring the need to rein in spending, Kyl pointed to the controversial House GOP budget authored by Rep. Paul Ryan, and said even that would add $5 trillion to the debt over the next decade. "Obama would add $12 (trillion) over the same period of time to our debt," Kyl said, disputing claims that the Republican plan is "radical."

McConnell said that from his perspective, anything that resembles a tax hike won't pass.

"Throwing more tax revenue into the mix is simply not going to produce a desirable result and it won't pass," he said on "This Week." "I mean, putting aside the fact that Republicans don't like to raise taxes, Democrats don't like to either."