WH: "Significant" deal possible on deficit, debt ceiling

House Republicans held a vote on a bill they unanimously oppose - to raise the debt ceiling with no strings attached. CBS News Congressional correspondent Nancy Cordes reports.

White House spokesman Jay Carney said today that a "significant deal remains possible" on cutting the deficit and raising the debt ceiling, although he emphasized that reaching an agreement on deficit reductions would require a "balanced approach."

In a White House press briefing, Carney told reporters that "everybody believes a significant deal remains possible" - but that such a deal would necessarily include tax increases, or the elimination of tax breaks and loopholes, for major corporations and high-earning Americans.

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

Ongoing negotiations led by Vice President Joe Biden fell apart late last week after Republicans and Democrats remained unable to compromise on the issue of raising taxes.

And while President Obama on Monday stepped up his personal engagement in the negotiations - meeting separately with Senate Majority Leader Harry Reid, D-Nev., and Senate Minority Leader Mitch McConnell, R-Ky. - the question remains as to who, if anyone, will be willing to budge on the issue.

Reid described his conversation with the president as "productive" and emphasized that a bipartisan solution was the only way forward.

"Neither party should confront this crisis alone and no one will be successful unless we confront it together," Reid said.

But he emphasized his hope that "my Republican colleagues will put the economy ahead of politics."

Prior to his meeting with Mr. Obama on Monday, McConnell reiterated his opposition to any form of tax hikes as a means to a deal.

"I intend to ask the president what he is prepared to do outside of raising taxes about the massive deficits and debt that have accumulated on his watch," McConnell said. "Let's start by taking both proposals off the table and focus on what can actually pass Congress and what will actually spur the private sector in our future and create jobs."

Increasing tax revenues, McConnell said, was "politically impossible."

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

Reid, meanwhile, urged Republicans to "set aside their desire to please the Tea Party and defeat President Obama" in the interest of the greater good.

"We owe the country our commitment to do at least the small things," he said.

The Obama administration has urged Congress to raise the debt limit as soon as possible in order to prevent the country from defaulting on its loans for the first time in American history. The Treasury Department has taken what it calls "extraordinary measures" to stave off economic catastrophe since the U.S. hit its limit on May 16, but Treasury Secretary Tim Geithner has repeatedly warned that those measures will only get the country through August 2.