A week away from Washington with appearances at parades, barbecues and picnics did not push senators any closer to agreement on how to deal with expired federally subsidized student loan rates.

Senate Majority Leader Harry Reid, D-Nev., filed cloture Monday on a Democrat-sponsored one-year extension of the expired fixed rate of 3.4 percent for subsidized Stafford loans, likely setting up a Wednesday procedural vote. But the politics around the issue are much more complicated, as Democrat Joe Manchin III of West Virginia and independent Angus King of Maine, who caucuses with Democrats, are set to present the details of their deal with Senate Republicans at the party’s lunch Tuesday. They, too, would like a vote on their plan, but no assurances had been made as of Monday that they would get one.

The split among Democrats largely stems from a move months ago by the Obama administration to present compromise policies in its annual budget, frustrating congressional Democrats and opening the door for Republicans to get policies they want using the framework as support. The plan introduced by Manchin, King and Senate Republicans largely resembles the White House proposal that would peg rates to the 10-year Treasury notes. Democratic Sen. Thomas R. Carper of Delaware also supports the bill.

The issue also has become a prime target for cross-Dome fodder; House Republicans have approved a bill that is a non-starter for Democrats but still can say they passed something as the Senate failed to come together around any plan with a filibuster-proof majority.

“The House legislation is worse for students than doing nothing at all. Under the House plan, as interest rates start to rise, student loan rates will rise with them. Soon, loan rates will be more than double,” Reid said as he opened the floor Monday after a 10-day break. “To find a responsible solution to the student loan issue — and every other major issue facing this Congress — the speaker should work with his Democratic colleagues instead of against them.”

Reid’s point on student loans was only a small portion of a speech broadly attacking House GOP leadership for embracing the “Hastert rule,” the unofficial Republican edict that no bill should come to the floor or pass without a majority of support from the majority caucus.

For his part, Boehner said Monday at a press availability with college students on the Capitol steps that the onus was on Senate Democrats to resolve their issues, given that Republicans had passed a bill. The previous subsidized loan rate of 3.4 percent doubled to 6.8 percent on new loans while lawmakers were on vacation.

“It’s time for the president to lead. It’s time for him to bring Senate Democrat leaders together and develop a solution. The House has done its job. It’s time for the Senate and the White House to do its job,” Boehner said.

But the White House is not jumping to assist congressional Democrats, and their position now does not quite match up with the position the administration laid out in its budget, making the president’s involvement in the issue even more complicated.

On Monday, White House Press Secretary Jay Carney said administration officials expect Congress to fix the problem quickly and he said rates could be patched for students retroactively.

“We believe that it can be done. The differences are not that significant. There is a way to do this that’s retroactive so that students are spared from having their rates double,” Carney said. “We need to do it in a way that students are guaranteed a low rate … so that they’re not overcharged … in order to pay down the deficit. Our views on that are clear.”

Of course, it’s not that clear because the White House’s own proposal is a non-starter with Congressional Democrats because it, like the Manchin-King Senate GOP compromise, does not cap rates in the likely event that interest rates rise in better economic times. As it stands now, the federal government will net a $51 billion profit from student loans this year from already enacted law. The student loan framework proposed in the president’s budget would raise $6.7 billion over 10 years.

The legislation from Senate Republicans Manchin and King, like the Obama proposal, would peg all newly issued student loans to the Treasury 10-year borrowing rate plus 1.85 percent for subsidized and unsubsidized undergraduate Stafford loans, plus 3.4 percent for graduate Stafford loans and plus 4.4 percent for PLUS loans.