Senate Democrats and Republicans are cautiously optimistic about their ability to strike a deal on a $5.9 billion student loan package less than three weeks before federal loan interest rates are set to double.

If the Senate approves a deal, it would likely be pegged to some iteration of an offer made late last week by Majority Leader Harry Reid (D-Nev.). Senate passage would in turn put pressure on the House to follow suit so Republicans can avoid being blamed for inaction.

Both sides have tried turning the student loan issue in their favor. Early last month, Democrats pushed a bill that failed on party lines, as did a GOP version. But Republicans helped shift the narrative by sending a letter to the president offering to offset the bill with some of the president’s own proposals. One of the GOP options was similar to a House-approved bill that would rescind money from the 2010 health care law — a nonstarter with Democrats. But the second alternative was a starting point for Reid’s offer; it would reform and increase employer pension payments. Democrats had previously sought to pay for the bill by closing a tax loophole that allows some wealthy people to pay less in Social Security taxes.

Democrats are now waiting to hear from Minority Leader Mitch McConnell (R-Ky.) to determine how to proceed. And while aides to both leaders suggested the two have not spoken directly on the matter, both sides are more positive about the prospects of success than they were just a week ago.

“While we still haven’t heard from the White House on our bipartisan proposal, we are encouraged to see the majority leader drop his insistence on taxing job creators,” a McConnell spokesman said in a statement. “We will review these new proposals and hope that they will finally review the bipartisan proposals we sent a week ago. But bottom line, now that Democrats are willing to take this issue seriously, and not just use students as props, we may be making progress.”

Student loan rates are set to double from 3.4 percent to 6.8 percent by July 1. The Senate is debating a farm bill, which could be on the floor for weeks. And the House is on recess, so time to work out a deal is running short. Speaker John Boehner (R-Ohio) has said that the lower rates could be applied retroactively should Congress fail to act before the deadline.

In Reid’s letter to Republican leaders Friday, he outlined a two-pronged way to pay for continued lower rates by creating fewer tax deductions for pension contributions and increasing premiums that employers pay into the Pension Benefit Guaranty Corp.

“The combination of these two proposals will provide sufficient resources to fund both a one-year extension of the current student loan interest rate and reauthorization of the nation’s surface transportation programs,” Reid wrote in the letter. The highway measure has also been stalled and needs to be reauthorized by the end of the month.

“My preference would be to use the funds raised by these two proposals to pay for both measures, and pass them immediately — since, as you know, both are critical to the economic security of middle-class families, and both must be addressed before the end of June,” Reid said.

The offset could be tricky to enact as is, however, because the increased contributions to the PBGC are already included in the pending highway bill, which was approved by the Senate but is now floundering in conference committee.

Moreover, the administration has been cool to the idea of using increased pension payments for anything other than deficit reduction.

In a statement provided to the Senate Finance Committee in February, Treasury Secretary Timothy Geithner told Sen. Mike Enzi (R-Wyo.) that the PBGC funds should not be used for purposes other than paying down the debt.

“The Administration proposes that the increases in PBGC premiums reduce the deficit and not be used for other purposes. As noted earlier, the increase would increase the PBGC’s capacity to meet its commitments without taxpayer funds,” Geithner said.