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Both Harkin and Reed met with Durbin, a member of Democrats' leadership team, during the meeting late Wednesday.
The administration said the earlier vote would not inevitably consign students to higher rates.
"I wish we would have got this done before July 1 but I remain very optimistic that we're going to get to a better place for students," Education Secretary Arne Duncan said.
"We're going to get it done sooner than later," he told reporters at a department event about summer reading.
Interest rates on student loans doubled to 6.8 percent July 1 because Congress didn't act. After Wednesday's vote, the political sparring continued.
"Today's vote is just another example of how out of touch Republicans in Congress are with the struggles of everyday American families," said Sen. Patty Murray, D-Wash.
Rep. John Kline, chairman of the House Education and the Workforce Committee, similarly blamed Democrats.
"Right now, millions of students trying to prepare for college and apply for financial aid are facing higher interest rates - all because a cadre of Senate Democrats is completely unwilling to compromise," said Kline, R-Minn.
The rate increase does not affect many students right away. Loan documents generally are signed just before students return to campus, and few students returned to school over the July Fourth holiday. Existing loans were not affected, either.
During last year's presidential campaign, lawmakers from both parties voted to keep interest rates on subsidized Stafford loans at 3.4 percent. Yet this year, without a presidential election looming, the issue seemed to fizzle and the July 1 deadline passed without action.
"It's like 'Groundhog Day,' trying to fix this problem again," said Sen. Kelly Ayotte, R-N.H.
The White House and most Democratic senators favored keeping the rates at 3.4 percent for now and including an overhaul of federal student loans in the Higher Education Act rewrite lawmakers expect to take up this fall.
The House has passed legislation that links interest rates to financial markets. House Republicans were opposed to a one-year extension, meaning the Senate vote might not have fared well with them.
"Republicans acted to protect students from higher interest rates and make college more affordable, yet Senate Democratic leaders let student loan interest rates double without passing any legislation to address the issue," House Speaker John Boehner, R-Ohio, said after the vote.
The leader of one young adult advocacy group was more direct in his criticism.
"The White House and Congress seem to be competing with each other over who can screw over students worse," said Evan Feinberg, president of the nonpartisan Generation Opportunity. "And Senate Democrats are clearly winning."