Updated: 6:25 p.m.

President Barack Obama invited Congressional leaders from both parties to the White House on Thursday with the intention of working out a final agreement to raise the debt ceiling and reduce the deficit in the next two weeks, he said Tuesday during brief remarks.

Although Obama asked Congressional leaders to leave ultimatums and political rhetoric at the door, he laid down his opposition to a short-term deal to avoid default. The Treasury Department forecasts that the nation’s cash situation will become critical Aug. 2.

“I don’t think the American people sent us here to avoid tough problems,” Obama said, calling for trillions of dollars in savings over the next decade by targeting domestic, defense and entitlement spending, as well as changes to the tax code, which Republicans have rejected. Both parties will need to get out of their “comfort zones,” the president said.

Speaker John Boehner shot back in a statement that the tax changes are a non-starter.

“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,” the Ohio Republican said. “The American people simply won’t stand for it. And their elected representatives in Congress won’t vote for it. 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. Our focus should be on getting our economy back on track by making the spending reductions and structural reforms necessary to address our nation’s out-of-control debt. We can do so without raising taxes on America’s small business job-creators.”

Senate Minority Leader Mitch McConnell said he viewed Thursday’s meeting as a chance “to talk about what’s actually possible.”

“I view it as an opportunity to know whether or not the President will finally agree to a serious plan to reduce the deficit,” the Kentucky Republican said in a statement. “Or if in the middle of a debt crisis, he’ll insist on more stimulus spending; whether in the middle of a jobs crisis, he’ll continue to insist on hundreds of billions in tax hikes that we know — and he has acknowledged — will kill jobs. Republicans in Congress believe that finding a way to reduce the deficit and prevent Medicare’s bankruptcy should be the goal. These discussions are not about rich and poor or an election but they’re about making Washington take the hit and make some tough choices for a change — not the taxpayers and job creators.”

Obama said he saw progress from discussions between the administration and party leaders over the July Fourth weekend. “Greater progress is within sight,” although “real differences” remain, he added.

Senate leadership aides in both parties confirmed that Thursday’s meeting will be bipartisan and bicameral, including Congress’ top eight leaders.

Obama does not plan to accept Senate Majority Leader Harry Reid’s request to meet with Senate Democrats on Wednesday, Press Secretary Jay Carney told reporters after Obama’s remarks. “Thursday is the next meeting we anticipate,” Carney said.

Meredith Shiner contributed to this report.