Washington ? “We’re back for another fun-filled week.” That was the sardonic opening comment of House Majority Leader John Boehner on Tuesday as he faced a roomful of reporters at the start of yet another testing period for the embattled congressional Republicans.

The week before, Boehner had barely managed to quell a rebellion from the big and influential bloc of Appropriations Committee Republicans, angry that their precious “earmarks” were targeted for reform in the leadership’s lobbying bill.

By invoking the personal prestige of Speaker Dennis Hastert, Boehner managed to clear the bill for floor action – and Wednesday, he saw it pass by a shaky four-vote margin.

But the bill was roundly condemned by Democrats and independent reform groups as an inadequate answer to the Abramoff scandals and the bribery conviction of former Republican Rep. Randy “Duke” Cunningham.

So when Boehner told reporters he was proud of it as a “comprehensive response” to the need for accountability in government, eyes rolled.

Then it was on to other topics, and the Ohio Republican went searching for safer ground.

Gasoline prices and energy legislation? Not here. Asked about the previous week’s talk of a $100 rebate to motorists to make up for $3 a gallon gas, he said his constituents found it “insulting.” The idea was “stupid,” he said, not caring that it had come from the mouth of his Senate counterpart, Majority Leader Bill Frist of Tennessee.

Port security? In the aftermath of the blown-up Dubai ports deal, Democrats were pressing for U.S. inspection of every cargo container coming into the U.S. Impractical, Boehner said. Random checks will have to do.

How about a budget for the government? Just before the Easter recess, Boehner had to pull the Republican budget resolution off the floor without a vote, because no agreement could be reached between conservatives appalled by the level of deficit spending and moderates resisting further cuts in education and health care. “There are a lot of conversations” about how to get it back on track – but no agreement yet, he said.

At this point, halfway through his weekly meeting with House reporters, the thought must have crossed Boehner’s suntanned brow that he might be otherwise occupied. At the start of the year, when Tom DeLay stepped down as majority leader to fight corruption charges in Texas, Boehner was something of a long shot to win the three-way contest against Roy Blunt of Missouri and John Shadegg of Arizona.

But he pulled off a second-ballot victory in the Republican Conference, and was catapulted into the leadership from his comfortable position as chairman of the Committee on Education and the Workforce.

Now, instead of doling out money to colleges and school districts, he has the whole mess on his hands – trying to satisfy a president with sinking support but ambitious goals such as making his tax cuts permanent, while holding together a congressional party increasingly nervous about keeping its majority in November.

And, oh yes, one other thing: the war in Iraq. As I confirmed again on a visit to Ohio last week, the casualties of that war – the group deaths of Marines and Army reservists plucked from their Ohio hometowns for repeated tours – have triggered a popular backlash more worrisome to Republicans than the scandals that have destroyed the standing of Gov. Bob Taft and jeopardized the whole state GOP ticket.

Hence the surprise announcement from Boehner that he has decided the House should have a full-scale debate on Iraq policy sometime this spring, perhaps before the Memorial Day break.

Why, he was asked, reopen the issue at this late date? “It is of great interest to our constituents,” he said, “and the House should work its will.”

How will the debate be framed? That will be up to Henry Hyde, the venerable chairman of the Foreign Affairs Committee, Boehner said, passing the hot potato to the 82-year-old World War II veteran who is retiring from Congress this year.

As Boehner surely knows, the Democrats hope to knock off Hyde’s normally Republican Chicago suburban district with a badly wounded female Iraq War veteran, Tammy Duckworth. Visiting the district last week, I was told by an influential Republican, “Hastert’s office is checking up on that race every week.”

Wherever you look, there’s no relief in sight for John Boehner – or the Republicans.