Rep. Chris Van Hollen, D-Md., ranking member on the House Budget Committee, gestures during a news conference April 7 on Capitol Hill in Washington. (Alex Brandon/AP)

After two weeks of sometimes-tumultuous meetings at home with constituents over the Republican proposal to privatize Medicare, lawmakers return to the fiscal wars this week, bracing for a lengthy battle over the nation’s solvency.

While Congress begins taking up proposals that are designed more to score political points than seriously address the national debt, the critical action will be happening behind closed doors.

President Obama starts it off Monday night by hosting a dinner party for a bipartisan collection of congressional leaders and top lawmakers from various House and Senate committees. Then on Thursday, Vice President Biden brings congressional leaders to Blair House for the first of what could be many discussions about how to reach a deal on the debt limit and then about an even longer-term issue: Medicare and Medicaid.

Congress must consider whether to raise the federal debt ceiling beyond $14.3 trillion in exchange for still-undefined budget-tightening — a debate that is certain to linger well past the preliminary deadline of May 16. That has already prompted Treasury Secretary Timothy F. Geithner to use accounting moves that would allow the United States to continue to make payments without exceeding the debt limit. But he would run out of possibilities in early July.

Setting the stage for negotiations that could last well into the summer, Democrats and Republicans criticized one another Sunday over which actions to attach to legislation extending the debt limit, with Democrats adamant that higher taxes on the wealthy and revoked tax privileges for oil companies be a part of a broad deficit-reduction package. Most Republicans refuse to consider higher taxes as part of any final deal and demand that the focus be on slashing entitlement spending.

“A lot of people think this is sort of like the magic fairy dust of budgets, that we can just make a small amount of people pay some more taxes and it will fix all of our problems,” House Budget Committee Chairman Paul Ryan (R-Wis.) said on ABC News’s “This Week With Christiane Amanpour.” “Well, let’s keep our eye on the ball. The eye on the ball is spending. And the sooner we get this thing under control, the better off everybody is going to be.”

Rep. Chris Van Hollen (Md.), the top Democrat on the budget panel, countered on CNN’s “State of the Union”: “The idea that we should come up with a balanced deficit-reduction plan is right. But what’s wrong is to say that if one side doesn’t get 100 percent of what it wants in terms of coming up with that plan that they will put the entire economy at risk.”

The talks being hosted by Biden have already been mocked by both parties in Congress. Some question how a group made up of lieutenants — Obama, House Speaker John A. Boehner (R-Ohio) and Senate Majority Leader Harry M. Reid (D-Nev.) are all sending subordinates — can reach deals on the most critical fiscal issues facing the nation.

“We cannot keep delegating these tough decisions to other people. Leaders need to lead,” Ryan said of the so-called Biden commission in an interview Friday with Bloomberg Television.

Looming large over these White House-led meetings is the bipartisan work of an ad hoc group of six senators, three Democrats and three Republicans, who are trying to cinch their own agreement, which could come before week’s end.

They have no official mandate, but members of the “Gang of Six” represent a possible game-changing moment because of what they could do to the political dynamics of the fiscal debate. These senators include Tom Coburn (R-Okla.), one of the chamber’s most pure conservatives, and Richard J. Durbin (D-Ill.), the majority whip who is considered Obama’s closest ally in the Senate. They are believed to be working off the report from the president’s fiscal commission, which called for slashing $4 trillion from projected deficits over the next decade through a combination of spending cuts and increased revenue through higher taxes. Durbin and Coburn served on the commission, and despite a bipartisan vote of support on the report, Obama cast it aside and congressional Republican leaders have done little with it.

Reid and Durbin’s internal rival, Sen. Charles E. Schumer (D-N.Y.), the No. 3 leader, have been somewhat dismissive of the Gang of Six. They have also disparaged some of the fiscal commission’s recommendations, including raising the Social Security retirement age to 69 and cuts to Medicare and Medicaid, and have focused their rhetorical attacks on the House Republican budget proposal for its privatization of Medicare.

Reid hopes to schedule a vote on the House-passed budget to drive a political wedge between the more conservative House Republicans and a collection of more moderate Senate Republicans. But Senate Minority Leader Mitch McConnell (R-Ky.) has countered with his own plan to force a vote on Obama’s original budget proposal, which was widely panned upon its mid-February release as far too timid in dealing with the nation’s swelling red ink.

The likely outcome: an embarrassment to both parties in a pair of failed votes.

The House is expected to move first on the debt limit, but GOP aides said there is no consensus yet on what sort of mandatory changes to spending would be attached to the legislation. Closed-door talks over the next two weeks are geared toward producing some level of consensus, but in the meantime, Boehner expects to hold a series of votes over the next 10 days on oil exploration as gasoline prices soar to more than $4 a gallon.

Democrats may be willing to accept some spending constraints in exchange for the debt ceiling vote, as both Obama and Reid have signaled support for a “trigger” mechanism that would impose deficit savings if certain fiscal targets were not met in the years ahead. But Democrats would demand that tax increases also be a part of the discussion, and they said Sunday that Republicans were risking the failure of the entire financial system by so far refusing to consider such a plan.

“It would be disastrous for the American economy” if the debt vote failed, Van Hollen said. “It would put people back out of work. It would make the last recession look like a cakewalk. And so I hope wiser heads will prevail as we move forward, because you cannot risk the full faith and credit of the United States.”