The Senate returned to Congress Tuesday after canceling its week-long July 4 recess to work on a deal to raise the debt limit, but so far on the schedule is a nonbinding resolution by Democrats expressing a sense of the Senate that households earning $1 million or more need to make "a more meaningful contribution to the deficit reduction effort."

Already a non-starter for Republicans, the august body won't even vote on the resolution until later this week but the timing could be affected by President Obama's meeting with eight leaders from both parties at the White House Thursday, a meeting the president said Tuesday was intended "to drive toward a final agreement" on the terms of increasing the debt limit beyond its $14.3 trillion ceiling.

Obama also rejected talks of a short-term debt limit increase that would give negotiators more time for a long-term deal, saying Congress should not "kick the can down the road."

"I don't think the American people sent us here to avoid tough problems," he said. "It's in fact what drives them nuts about Washington, when both parties simply take the path of least resistance. And I don't want to do that here."

"I believe we have a big opportunity to do something big," he added. "To tackle our deficit in a way that forces our government to live within its means, that puts our economy on a stronger footing for the future and still allow us to invest in that future."

But the White House and Republicans so far have been unable to overcome the sticking point on slashing tax deductions and subsidies for upper-income earners and corporations. Democrats say tax increases must be included in any deficit-reduction deal. Republicans say no increases, period.

"We're not dealing just with talking points about corporate jets or other 'loopholes,'" House Speaker John Boehner said in a statement after the president's remarks. "The legislation the president has asked for -- which would increase taxes on small businesses and destroy more American jobs -- cannot pass the House, as I have stated repeatedly."

"I'm happy to discuss these issues at the White House, but such discussions will be fruitless until the president recognizes economic and legislative reality," he said.

House Majority Leader Eric Cantor, R-Va., who said he plans to tell the president at Thursday's meeting that a tax increase simply will not pass the House, blamed Democrats for the stalemate.

"Contrary to the president's unserious claims last week, House Republicans aren't objecting to this loophole or that," Cantor spokeswoman Laena Fallon said in a statement. "We oppose raising taxes on families and small businesses at a time when we all should be focused on growth and job creation."

The Treasury has set an Aug. 2 deadline for getting a deal done or the nation possibly facing default on its loans for the first time.

"This crisis is not a new problem. It's been around for months," Senate Majority Leader Harry Reid, D-Nev., said Tuesday. "We no longer have months or even weeks to avert this catastrophe. We have days."

That's why Senate Republicans expressed disappointment in Reid's nonbinding resolution supporting tax hikes.

"Instead of bringing forth a budget plan, a debt limit proposal, or a Balanced Budget Amendment, the majority leader is wasting valuable time on a political stunt that will do nothing to substantively address our debt problem," Sen. Kelly Ayotte, R-N.H., said in a statement. "We cannot tax our way out of more than $14.3 trillion in debt."

Republicans believe reining in excessive federal spending is the trick to getting America's fiscal house back in order.

"This isn't a trade-off of spending cuts for tax increases. The area where we should compromise is where we cut spending," Sen. Pat Toomey, R-Pa., told Fox News. Toomey said Democrats in Congress and the administration know that a $3.6 trillion budget is just too big, especially when the government is working with a $1.4 trillion deficit.

"Presumably they acknowledge ... that there are areas they'd like to cut. There are areas I'd like to cut. Probably not the same areas," he said, adding that that's how the negotiation should work.

Senate Republican leader Mitch McConnell said the only way Republicans will raise the limit on the national credit card is "if Democrats agree to change their ways -- so we don't end up with the kind of situation here that we're witnessing in Greece."

"And make no mistake: that's exactly where we're headed if we don't do something significant now," he said.

White House aides told Fox News that the president has been talking about money-saving improvements to both Medicare and Medicaid since April. The New York Times reported Tuesday that the White House has offered to cut tens of billions of dollars from the programs if Republicans agree to raise taxes.

Fox News' Jim Angle and Trish Turner contributed to this report.