The House will vote Thursday on whether to adjust an obscure tax provision that is widely expected to be a huge burden on government contractors and cost jobs should it take effect as scheduled in 2013.

Republicans support the change. So do Democrats. President Obama likes it so much that he tucked it into his $447 billion American Jobs Act.

And so it might seem that passing the legislation would be easy.

But that’s not how things tend to work in this Congress, where even minor issues on which there is agreement somehow turn into referendums on the major divisive matters of the day.

“It unfortunately underscores the worst of the situation we’re in now,” said Joel Zingeser, director of corporate development for Rockville-based Grunley Construction, a government contractor pushing for the tax change. “Because it’s one thing if one side has a point of view and the other side has a different point of view and you have to find a way to come together. But this . . . you say: Why can’t they just get it done?”

Congress is likely to approve the change eventually, but with a degree of difficulty that is now common in Washington. The reasons are familiar: It costs some money — the Congressional Budget Office estimated $11.1 billion over the next decade.

And in figuring out how to pay for it, both parties have retreated to the same battle crouches over spending and taxes that have defined Washington’s political war in recent years.

The tax provision is not exactly an economy-reshaping proposal. In fact, in the real world it wouldn’t actually do anything at all. Instead, it would repeal a tax provision enacted in 2006 that has not taken effect. Delayed twice, it is now scheduled to go into effect in January 2013.

Faced with a series of studies that showed that vendors who do business with the government routinely skimp on their taxes — potentially to the tune of billions of dollars of lost revenue — Congress agreed in 2005 that local, state and federal governments should start withholding 3 percent of payments to contractors.

The businesses would get the money back in refunds at tax time if they owed less than 3 percent.

But then state and local governments complained that the withholding program could be expensive to administer. And contractors argued that not all of them should be punished for the sins of a few tax cheats.

“Totally irrational,” Zingeser called the idea.

“A wet blanket” hanging over small businesses, House Speaker John A. Boehner (R-Ohio) said Tuesday.

“A burden on government contractors,” the White House declared Tuesday in announcing that the president supports the House bill.

And yet, somehow, even this proposal has gotten hung up as a proxy for a larger debate.

For example, House Republicans on Thursday are expected to propose paying for the repeal by tightening Medicaid and Medicare eligibility and reducing federal health-care costs. The White House said Tuesday that it supports the idea, which could save as much as $13 billion over the next 10 years, but many congressional Democrats are opposed.

“I don’t think it’s as bipartisan as the Republicans would like to couch it, by any stretch of the imagination,” House Democratic Caucus Chairman John B. Larson (Conn.) said Tuesday.

He said that congressional Democrats have a “long-standing concern” about the health-care proposal. They could support it, he said, but only in the context of a big deal with Republicans to reduce the deficit that also would include tax increases.

Senate Republicans last week suggested paying for the idea by cutting $30 billion from other spending programs. That drew a veto threat from the White House. Democrats countered with a proposal to close corporate tax loopholes. Republicans have said they would consider those ideas, but only in the context of a big deal with Democrats to reform the tax code.

“Watching Washington, sometimes it seems to be that nothing gets done — until it happens,” said Mark Zandi, chief economist for Moody’s Analytics.

Zandi said that the withholding repeal would ultimately be approved, even though he regards it as such a minor provision that he did not include it as part of his analysis of the president’s jobs plan, which he concluded would create 1.9 million positions.

“I don’t think it’s meaningful in terms of jobs,” he said. “It’s more trying to clean up something that needs cleaning up.”

The cleanup should be relatively easy, given the support the repeal has drawn so far; 207 Republicans and 62 Democrats, nearly two-thirds of the House, have signed on as co-sponsors.

But it may take a little time.

Said Rep. Wally Herger ­(R-Calif.), who supports the repeal: “Nothing we do in Congress is easy.”