Budget-watchers everywhere seem to be asking two questions this week as Congress returns to Washington from a weeklong recess. The first — whether there’s going to be a federal government shutdown — has been debated almost since the day after last year’s midterm elections. The newer and far more interesting question is whether Congressional Republicans have any chance of getting out of the budget corner they’ve painted themselves in without inflicting serious political damage on themselves.

A similarly tough budget situation played out in the late 1970s when the federal budget process as we know it was just getting started. The Republican members of the House Budget Committee made it clear year after year to then-Chairman Bob Giaimo (D-Conn.) that there was no way they would vote for any budget resolution that didn’t completely capitulate to GOP demands. Their position forced Giaimo to move to the left with his budget resolutions to win the support of enough Democrats so he could move the bills to the House floor. That gave Democratic Reps. Elizabeth Holtzman of New York (my boss at the time), Parren Mitchell of Maryland and Louis Stokes of Ohio enormous — some might even say undue — influence over the committee’s work as Giaimo moved in their direction on military spending and other policies to get their votes.

Giaimo did this at great personal political peril. There was far more support in his district for military spending than the levels in his budget resolutions, and he often threatened to vote against Holtzman, Mitchell and Stokes’ demands if they went too far. Nevertheless, he had no choice but to move in their direction because committee Republicans refused to consider a compromise. Because of this, the GOP always ended up with even less of what it wanted than otherwise would have been the case.

Today’s GOP budget dilemma is similar in many respects to the one it imposed on itself 30-plus years ago. This time the tea party wing of the Republican Party in the House has repeatedly let its own leadership know that a budget compromise is unacceptable. These fiscal conservatives say they will only vote for a continuing resolution for the rest of fiscal 2011 that includes deep spending cuts and appropriations riders on health care reform and other issues. This has presented Speaker John Boehner (R-Ohio) and Majority Leader Eric Cantor (R-Va.) with a Giaimo-like choice: Completely capitulate to the tea party or move toward the Democrats to get enough votes to pass a continuing resolution in the House.

But this year’s budget corner is significantly tighter than the one Giaimo was in three decades ago.

Although he would have to work hard to get the votes, Giaimo knew that the Democratic-controlled Senate would modify his budget resolution and that a conference report with those changes would ultimately be adopted. But based on the budget negotiations and votes that have already taken place this year, Boehner and Cantor have to assume that the Senate and White House won’t accept a tea-party-supported continuing resolution. A government shutdown that might well be blamed on Boehner, Cantor and the Republican Party would then occur.

Giaimo also knew that, no matter what happened on the budget, the Holtzman-Mitchell-Stokes wing of the Democratic Party would work with the Caucus on other issues and wouldn’t challenge him or Speaker Tip O’Neill (D-Mass.) either in a primary or for a leadership position. Boehner and Cantor have no such assurances. Indeed, given some of the doubts that tea party folks have already expressed about the House GOP leaders, it’s hard to see how they will be brought back into the Republican fold on any other issue if Boehner and Cantor modify the CR to attract Democratic votes.

Giaimo was fortunate in that he was only dealing with one issue — the budget resolution. Now, however, the GOP leadership has to be very mindful that, by its own choosing, the debate over the continuing resolution will be followed in very short order by difficult debates on two other mega budget issues: the fiscal 2012 budget and an increase in the federal debt ceiling. Moving away from the tea party on the first issue very likely will mean losing it on the other two unless there’s total capitulation, and that would probably doom any chance for a budget resolution this year and greatly annoy the bond market.

This leads back to the question of whether there will be a government shutdown. If courting Democratic votes for the continuing resolution will cause an angry and potentially irrevocable GOP split on the other budget issues, then going with a tea-party-preferred continuing resolution will be the House GOP leaders’ politically correct choice even if it is more than likely to lead to a shutdown. If a shutdown then demonstrates to the tea party that the no-compromise position is damaging, the leadership might find its way out of that tight budget corner after all.

Stan Collender is a partner at Qorvis Communications and founder of the blog Capital Gains and Games. He is also the author of “The Guide to the Federal Budget.”