Kline charged the Senate had "actively" blocked the "president's plan" and refused to consider the House bill, ABC News reported.
Student loan rates will increase from 3.4 percent to 6.8 percent on new subsidized Stafford loans July 1 if nothing is done.
Allowing rates to be set by the market would resolve the last-minute wrangling, he said.
"We're in this predicament because politicians put themselves in charge of setting interest rates, guaranteeing exactly this type of down-to-the-wire uncertainty for students and their families," Kline said. "What we need is a long-term solution that gets Washington out of the business of setting rates altogether.
Kline called on Obama to show more leadership in resolving the issue, noting that House Speaker John Boehner, R-Ohio, sent the president a letter this week asking him to get involved in the dispute.
"Because of our efforts," Kline said, " there are finally signs of progress toward a bipartisan plan for a long-term market-based solution, but we need to finish the job -- and do so soon."