The U.S. Senate on just approved legislation to link interest rates on student loans to the market, which would cut rates in the short term but potentially allow them to rise significantly within a few years.

The margin of the vote, 81 to 18, surprised supporters of the bipartisan compromise, given numerous expressions of opposition by Democrats. All but one of the Senate’s “no” votes were from Democrats (Republican Mike Lee of Utah was the one “no” from his party), many of whom voted for an alternative pushed by Sens. Elizabeth Warren and Jack Reed and another proposal that would have sunsetted the proposal before rates were likely to spike. (Note: This article has been updated from an earlier version to correct the vote breakdown.)

But with supportive statements issued within minutes of the Senate vote by leading House Republicans (Speaker John Boehner and Rep. John Kline, chairman of the House Education and the Workforce Committee) and Rep. George Miller, the senior Democrat on the House education panel, the measure seems sure to pass the House. The White House signaled President Obama’s support early Wednesday, virtually ensuring that it will become law.

…The vote also got strong support from higher education leaders. “While this bill is not perfect and we wish that rates could have been made even lower, it represents the best deal possible given the political realities of Washington,” said Peter McPherson, president of the Association of Public and Land-Grant Universities. “This measure keeps rates nearly as low as they were before July 1 for the immediate term, locks in interest rates for the life of each loan, and puts in place a cap to prevent rates from skyrocketing in the future.”In supporting the legislation as a reasonable compromise that will keep rates low in the near term but put student loan rates on a sustainable long-term path by letting them rise well above current levels as market rates rise, President Obama is crossing his party’s liberals, who complained bitterly that the legislation passed Wednesday will cost students hundreds of millions of dollars more over a decade than even the higher rates that took effect July 1 would.

Under the legislation, student loan rates would reset each July based on the previous May’s auction of 10-year Treasury bills. Undergraduate loans — those that are federally subsidized as well as those that are not — would be set at the Treasury rate plus 2.05 percentage points, while loans for graduate students would be set at 3.6 points above the Treasury rate, and loans for parents at 4.6 percentage points over the T-bill rate. The maximum rate would be capped at 8.25 percent for undergraduate loans, 9.5 percent for graduate student loans, and 10.5 percent for parent loans.