Debating loans this week, Republicans said one year of lower rates isn't long enough.
At their own weekly press conference Tuesday, Republican leaders likened the Democratic bill to the annual "doc fix," which Congress has passed each year to prevent a drop in reimbursement rates for doctors who treat Medicare patients.
"I think many of the Democratic senators have been busy with immigration and haven't had a chance to really read the bill," said Sen. Lamar Alexander, R-Tenn., a former Education secretary who has been working with Democrats on the GOP-supported bill.
"My hope is that as the Democratic senators look at the bipartisan proposal, they won't want to leave those 7 million students in middle-income families paying a 6.8 percent rate when they could be paying 3.6," Alexander said at Republicans' weekly press conference on Tuesday.
After the failure of Democrats' one-year fix, Ayotte pressed for a vote on the plan backed by Republicans and the three Democrats. On Tuesday, Carper, a Democrat who supports that plan, asked for the same.
So far, Democratic leaders have not scheduled a vote on the GOP plan, as the standoff continues.
ABC's John Parkinson contributed to this report.