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Senators wrapped up business Thursday and headed home for a vacation next week. When they return, they will face an early test vote on yet another student loan bill, offered by Majority Leader Harry Reid, Nevada Democrat.

Mr. Reid covers the $6 billion cost by changing a tax formula to catch what is called pass-through income. That’s where someone sets up a company and takes most of his income as company profits that pass through to him. That allows him to avoid paying Medicare payroll taxes on that pass-through income. Mr. Reid ends that option for those making $250,000 or more a year.

Democrats argued that the Republicans are quickly trying to backslide on this issue. While Mr. Obama’s proposed budget called for extending the interest-rate subsidy, the House GOP’s budget did not — and Republicans on the Budget Committee defeated an amendment that would have extended it.

At the White House, press secretary Jay Carney said the administration could support a number of different ways to pay for the extension, but said the president’s health care law should not be one of them.

“Let the election decide that. Let’s solve the student loan rate problem now and focus on pay-fors that are reasonable and acceptable,” he said.

But in a sign of the political overtones of every fight this year, Mr. Boehner took aim at the president’s two-day swing through college campuses.

Mr. Boehner said the trip was an attempt to manufacture a political issue. The Ohio Republican demanded that Mr. Obama’s campaign reimburse the federal Treasury for the costs of flying Air Force One on the trip — which Mr. Boehner said amounted to $179,000 an hour.

“This is the biggest job in the world, and I’ve never seen a president make it smaller,” Mr. Boehner said. “The president keeps attempting to invent these fake fights because he doesn’t have a record of success or a positive agenda for our country.”

Mr. Carney said the Obama campaign is following all rules that govern dividing political costs and official business costs, and he said previous presidents have done the same thing.

“There’s an effort to politicize this, an effort to hide the fact that they have a policy problem on their hands,” Mr. Carney said. “But our interest, the president’s interest, is ensuring that this matter be taken care of on behalf of American college students.”