After weeks of negotiations, Senators reached a deal Wednesday to retroactively reduce some student loan rates and to change how many federal loan rates are calculated.

Interest rates on subsidized Stafford student loans doubled from 3.4 to 6.8 percent July 1. The deal brings that rate back down and ties subsidized and unsubsidized rates to the market, with caps on individual loans.

Senators--including Manchin, King, Harkin, Durbin, Alexander, Burr, and Coburn--met at the White House on Tuesday with President Obama where student loans were discussed, according to Senate aides.

The deal is based on a proposal that had been crafted by a bipartisan group of senators, including: Sens. Joe Manchin, D-W.Va., Angus King, I-Maine, Lamar Alexander, R-Tenn., Tom Coburn, R-Okla., and Richard Burr, R-N.C.

Sen. Tom Harkin, D-Iowa, as well as other Senate Democratic leaders, had been pushing back against the deal being crafted by the senators, saying it reduced the deficit on the backs of students and would eventually lead to higher rates.

But the pressure grew this week, particularly after the White House meeting where Obama expressed support for the deal, according to a Senate GOP aide.

Harkin agreed to the deal during a Wednesday meeting in Senate Majority Whip Dick Durbin's office, several aides confirmed, and a Senate aide confirmed he will vote for the plan.

Harkin's support signals that the log jam over negotiations has been overcome. He chairs the Health, Education, Labor and Pensions Committee.

The deal ties loan interest rates to the 10-year Treasury note. Both subsidized and unsubsidized Stafford undergraduate loans would add 2.05 percent on top of the T-note with an 8.25 percent up-front cap on individual loans.

Graduate loans would add 3.6 percent to the Treasury note, with a 9.5 percent cap, and PLUS loans--available to graduates and parents of undergraduates --would have an additional 4.6 percent with a 10.5 percent cap. The Congressional Budget Office scores the proposal at about $700 million.

"We have a plan that ought to save students in 11 million families billions of dollars. And we've had a good discussion with Senator Harkin and Senator Durbin," Alexander said after the meeting in Durbin's office. "We'd like to be able to do this together, and we hope we can, and we hope we will come to a decision right away, because families need to make their plans."

"The House can hopefully accept it, send it to the president, and it [can] all be done by the end of the month," Alexander added.

Several aides said a vote could come by next week.

The House passed a bill in May that also ties rates to the 10-year Treasury note with percentages on top but lacks upfront caps on individual loans and allows rates to fluctuate yearly. The White House budget plan also tied rates to the 10-year Treasury note but includes different additional percentages for subsidized and unsubsidized loans.

In recent weeks, Democrats had been warming to the idea of tying interest rates to a market instrument, particularly after a second attempt at freezing the 3.4 percent rate failed in the Senate in July. Unsubsidized loan rates have remained constant at 6.8 percent.

But Democrats had insisted that any deal include caps on individual loans, saying that as the economy improved, interest rates could soon exceed the 6.8 percent rate they had risen to on July 1. Such a cap had been missing in the initial compromise hashed out by Manchin, King, Alexander, Burr, and Coburn.

But then last week, several proposals, including one by the bipartisan group of senators and from the White House, included such a cap, setting off a back-and-forth with the CBO to adjust figures with the idea that a final deal would be deficit-neutral.