House Republicans recently passed legislation, the Interest Rate Reduction Act, H.R. 4628, which extends the current interest rate on student loans at 3.4 percent. If Congress does not act, the rate is set to double to 6.8 percent on July 1. 

Democrats are also pushing legislation to maintain the current rate at 3.4 percent, but their legislation pays for the extension by closing tax loopholes for shareholders of S-corporations that allow them to avoid payroll taxes on some of their income. 

"Republicans are making outrageous partisan attacks on the prevention fund," Harkin said earlier in his speech. "I find this deeply disturbing and disappointing."

"What they are proposing is bad public policy, it's bad priorities," Harkin said of Senate Republicans. He said that Republicans should join Democrats in supporting the Democrats' legislation, which he said makes some of the wealthiest Americans "put country first."

Sen. Lamar AlexanderAndrew (Lamar) Lamar AlexanderSanders wants pharma CEOs to testify on opioid crisis Trump expects us to trade clean air and water for updated infrastructure House GOP warming to ObamaCare fix MORE (R-Tenn.) spoke after Harkin, and said Republicans agree that the 3.4 percent rate should be maintained.

"We agree — by 'we' I mean Gov. [Mitt] Romney, the likely Republican nominee for president, President Obama, the House Republicans, I, others — that for the next year, we should keep the interest rate on 40 percent of the student loans at 3.4 percent for new loans," he said. "We agree on that. What's different is how we pay for it."

Alexander, who served as secretary of Education under former President George H.W. Bush, also argued that a bigger problem with student loans relates to how states have been forced to make budget choices given federal mandates. He said federal requirements to spend more on Medicaid have forced schools to raise tuition, which leads to larger student debt.

"Those federal Medicaid mandates are soaking up money that would otherwise go to public colleges and universities, and as a result of that the universities are raising tuition, and as a result of that loans are up," he said.

—Pete Kasperowicz contributed reporting.