Senate Majority Leader Harry Reid acknowledged Wednesday that the chances of a student loan deal passing the chamber this week are low.

“There is no deal on student loans that can pass the Senate because Republicans continue to insist that we reduce the deficit on the backs of students and middle-class families, instead of closing tax loopholes for the wealthiest Americans and big corporations,” the Nevada Democrat’s spokesman Adam Jentleson said. “Democrats continue to work in good faith to reach a compromise but Republicans refuse to give on this critical point.”

If the tax issue is indeed critical, then it seems unlikely any agreement can be reached.

But some negotiators were still working to reach a compromise on Wednesday.

Sen. Joe Manchin III, D-W.Va., has been trying for a student loan compromise with Maine Sen. Angus King, an independent who caucuses with Democrats, and several Republicans.

He told reporters Wednesday that his group essentially has an agreement, saying that he had “signed off” on it, although work continues.

It is unclear how much buy-in the proposal Manchin is working on would have. Don Stewart, a spokesman for Minority Leader Mitch McConnell, R-Ky., was quick to respond to Reid’s office in a statement.

“As a result of their obstruction, interest rates on some new student loans will increase next week. The Republican House has already passed legislation and Senate Republicans, along with the President, are ready to pass bipartisan student loan reform that will ensure that student loan rates don’t double on July 1st,” Stewart said.

On Tuesday, several senators hinted at what Reid and McConnell are now acknowledging, that student loan rates are likely to go up next week. However, some senators believe a retroactive bill could be adopted when the House and Senate return from their July Fourth recess.

However, as CQ Roll Call has reported, the principle problem in getting a deal has been Senate Democrats’ displeasure with President Barack Obama’s proposal, which is similar to the Senate GOP’s plan.

UPDATE, from WGDB’s lesser half, Shiner, at 5:10 p.m.: As anticipated, a bipartisan group of senators announced a student loan compromise. Manchin and King, along with Republicans Richard Burr of North Carolina, Tom Coburn of Oklahoma and Lamar Alexander of Tennessee unveiled a plan that looks close to the White House/Senate GOP framework.

Here’s the new Manchin/King/Burr/Coburn/Alexander formula, per a joint release:

“The Student Loan Certainty Act requires that, for each academic year, all newly-issued student loans be set to the U.S. Treasury 10-year borrowing rate plus 1.85% for subsidized and unsubsidized undergraduate Stafford loans; plus 3.4% for graduate Stafford loans; and plus 4.4% for PLUS loans. The interest rate would be fixed over the life of the loan and the cap on interest rates for consolidated loans would remain at 8.25%. The Congressional Budget Office has determined this legislation would reduce the deficit by $1 billion over ten years.”

Of course, that last deficit reduction piece is the rub. Typically, lawmakers are giddy when the CBO scores a bill as reducing the deficit. But Democrats had been hoping for a deficit neutral plan. On principle, they oppose the idea of using revenue from students to pay down the debt, although in practice, this is likely to happen under most plans that are politically viable at this point. It’s unclear how much tinkering with the formula would need to be done, given Reid’s comment, but the Senate plans to wrap its immigration bill this week and then will recess for July 4th, so the time is short and paths narrow to get a deal.