WASHINGTON — The Senate on Wednesday approved a bipartisan plan that would tie interest rates for college student loans to the financial markets, bringing Congress close to finally resolving a dispute that caused rates to double on July 1.

But the 81-18 vote, which drew overwhelming support from Republicans, masked deep divisions among Senate Democrats. Seventeen of them voted “no.”

Many liberals, who are upset that the plan would replace the fixed-rate subsidized federal student loan program, criticized their colleagues for leaving lower- and middle-income students vulnerable to swings in the market.

House Republicans, who had approved a plan similar to the one the Senate passed, although with slightly higher loan rates, are expected to pass the Senate bill before Congress leaves for its summer recess next week.