It would cost taxpayers thousands of dollars per borrower for the government to refinance student loans, according to the American Action Forum. In a new analysis, the right-leaning think tank calls the measure to allow students to refinance their college debt, proposed by Senate Democrats, "a great deal for private lenders, but a very bad deal for taxpayers."

The American Action Forum joins other conservatives in pushing back against the Bank on Students Emergency Loan Refinancing Act, which was introduced by Sen. Elizabeth Warren, D-Mass., and received an endorsement from President Obama Monday.

The bill would allow student borrowers to restructure old loans with higher interest rates to take advantage of the low rates currently charged. For the 2014-2015 school year, the rate on federal direct loans will be 4.66 percent. The rate was as high as 6.8 percent through the 2008 school year, before incremental decreases brought it to 3.4 percent in 2013, when the president signed a new law tying the rate to market interest rates.

A borrower with $10,000 in debt at a 6.8 percent rate who participated in the refinancing program would cost the government $1,280, according to AAF. A student with $25,000 in loans would cost taxpayers $3,201.

The average loan balance was roughly $25,000 for all age groups in 2012, according to the Federal Reserve Bank of New York. The average graduate in the class of 2014 had even more debt -- $33,000 according to Edvisors. Recent graduates, however, enjoyed lower rates on federal loans.

The Congressional Budget Office estimated that as a whole the Warren legislation would cost the government $51 billion, including for private loan refinancings, and it would result in roughly half, or $500 billion worth, of the outstanding volume of student loans going through the refinancing process.

The AAF calls the bill a "lose-lose" proposition, noting that the costs of the program are offset by a new tax on high earners. In addition to the fiscal costs of the bill, the AAF concludes, the legislation "does nothing to improve access for low-income borrowers, and threatens to exacerbate inequalities between more and less-informed students" who do not take advantage of the program.

Republican Sen. Lamar Alexander of Tennessee led the charge against the Warren bill Sunday, calling it a "political stunt" that would only give "some former students a $1-a-day subsidy to help pay off loans."

Democrats, however, have said that the roughly $1.1 trillion in student loans is a drag on the economic recovery, causing young adults to postpone or forgo home or auto purchases.

Top Democratic economic policymakers such as former Obama adviser Larry Summers and Federal Reserve Chairwoman Janet Yellen have warned the indebtedness of U.S. graduates might be holding back stronger economic growth.