Senate Majority Leader Harry ReidHarry ReidChris Murphy’s profile rises with gun tragedies Republicans are headed for a disappointing end to their year in power Obama's HHS secretary could testify in Menendez trial MORE (D-Nev.) on Monday set up the first procedural vote to advance a student loan-refinancing bill.

The vote to end debate on the motion to proceed will likely occur on Wednesday.

It is unlikely that enough Republicans will join Democrats to advance the bill, which is paid for by raising taxes on millionaires. Senate Health, Education, Labor and Pensions Committee ranking member Lamar AlexanderAndrew (Lamar) Lamar AlexanderChildren’s health-care bill faces new obstacles Overnight Health Care: Schumer calls for tying ObamaCare fix to children's health insurance | Puerto Rico's water woes worsen | Dems plead for nursing home residents' right to sue Schumer calls for attaching ObamaCare fix to children's health insurance MORE (R-Tenn.) called the bill a “partisan political stunt” that includes a “class warfare tax.”

Sen. Elizabeth WarrenElizabeth Ann WarrenOvernight Finance: Lawmakers grill Equifax chief over hack | Wells Fargo CEO defends bank's progress | Trump jokes Puerto Rico threw budget 'out of whack' | Mortgage tax fight tests industry clout Michelle Obama is exactly who the Democrats need to win big in 2020 Wells Fargo chief defends bank's progress in tense Senate hearing MORE (D-Mass.) authored S. 2432, the Bank of Students Emergency Loan Refinancing Act, which would allow the nearly 40 million people with more than $1 trillion in student loan debt to refinance to today’s lower interest rates. She would pay for the bill by imposing a minimum tax rate on millionaires.

The Congressional Budget Office (CBO) determined that allowing former students to refinance their loans would cost $51 billions, but the tax increase on the wealthy would fetch $72.5 billion in revenue for the federal government, meaing a $20 billion net gain.

Democrats argue that allowing borrowers to refinance student loans to a lower rate, the way people currently can with car loans and mortgages, would give the middle class a “fair shot” and free up funds that could be put to better use elsewhere in the economy.

“Crushing student loan debt is keeping many young people from moving out of their parents’ homes, from saving for a down payment, from buying homes, buying cars, starting small businesses, saving for retirement, or making the purchases that grow our economy,” Warren said. “It doesn’t have to be this way.”

— Peter Schroeder contributed to this article.