As the student loan endgame neared, Democrats grumbled about the budget rules that make the bipartisan package work.

With an extra push from the White House, however, the bill seemed on track for passage.

“We’re going to enjoy it now and pay later,” Rhode Island Democrat Jack Reed said, citing the Congressional Budget Office determination that the deal announced last week would backload higher interest rates in later years. “The cost of fixing it goes up with each year.”

This manner of accounting is nothing new. The formula used to calculate payments to doctors who treat Medicare patients always assumes a huge cut in payments to providers in future years, a budgeting debacle that’s come to be blocked through the stopgap known as the “doc fix.”

Reed said he planned to offer an amendment with Sen. Elizabeth Warren, D-Mass., to cap the rates for students at 6.8 percent, instead of allowing them to float higher, with no real anticipation of success.

Health, Education, Labor and Pensions Chairman Tom Harkin, D-Iowa, signed on to the bipartisan deal last week, thinking that the short-term benefits of lower federal student loan interest rates outweigh the longer-term implications. Asked about the “doc fix” comparison, Harkin said he would explore changes in the future.

“Any law’s subject to change; this one is too,” Harkin said. “We don’t know how it’s going to work in the future in terms of interest rates or what interest rates may be, all we have to go on is CBO estimates and we all have to play by these — this rule-book. That’s why I want to take another look at it in the higher education act next year. Let’s see where the economy’s headed, let’s see where the interest rates are headed.

“The most important thing in terms of student loans is what’s going to happen to the trillion dollars hanging over their heads right now,” Harkin said.

White House officials, up to and including President Barack Obama, have pushed for the student loan compromise hashed out among a bipartisan group of senators. Republicans have been vocal in their support.

“Democrats need to finally allow the bipartisan student loan reform proposal to come to a vote this week, so we can pass it and ensure there’s one less Washington-created problem for young people to worry about in this economy. Because it’s tough enough out there for them already,” Minority Leader Mitch McConnell, R-Ky., said Tuesday on the Senate floor.

Democrats opposing the deal have directed varying degrees of ire at the Obama administration.

The White House released a fact sheet Tuesday showing short-term benefits of the plan, saying: “Under the compromise plan, nearly 11 million borrowers will see their interest rates decrease on new loans after July 1, 2013.” Education Secretary Arne Duncan then participated in a conference call supporting the package.

“The White House is being disingenuous and is trying to sweep under the rug big increases in interest rates for students and parents in the near future,” Sen. Bernard Sanders, I-Vt., said in a statement. “Because college costs are out of control and interest rates are rising, students are leaving college deep in debt or in some cases choosing not to continue their education because they cannot afford it.”

But Sen. Richard Blumenthal, D-Conn., was more reserved.

“I think the White House has the right intentions and great motives. I simply disagree on the caps and other essential features,” Blumenthal said.

He announced his opposition to the agreement July 19, in part because of what he called “variable low teaser rates” in the near term.

Speaking with reporters after Tuesday’s Democratic caucus lunch, Majority Leader Harry Reid, D-Nev., said he believes a majority of Democrats will vote “yes” when the final passage vote comes up, without expanding on his thinking.

About an hour earlier, Harkin told a group of reporters outside the lunch that it was too early to predict a whip count.

“I don’t know how this is all going to filter out,” Harkin said. “I mean, some people may want to express themselves on an amendment … and once they’ve expressed themselves they may then vote for the compromise.”

Harkin encouraged his colleagues to realize that the lower interest rates in the short-term made the package worthy of support, with the Iowa lawmaker noting he often finds himself voting for deals he wouldn’t have designed.

“I mean, chairmen sometimes have to reach compromises. I did that in agriculture bills, I’ve done that in a lot of other bills. I don’t get what I want just because I’m chairman,” Harkin said.