WASHINGTON — A Senate deal to lower the interest rate on most new federal student loans hit a snag yesterday when congressional researchers reported it would cost $22 billion over a decade.

A bipartisan group of senators had reached the agreement late Wednesday.

Similar to plans backed by the GOP-led House and the White House, their proposal would tie the interest rates on all student loans to the 10-year Treasury note, lowering rates in the short term and letting them rise as the economy picks up.

But the $22 billion price tag reported yesterday by the Congressional Budget Office hurts the deal’s prospects, given Republican opposition to raising taxpayer costs, said an aide to a GOP senator leading the talks.

Lawmakers have been in talks to bring down rates on subsidized Stafford loans, which shot from 3.4 percent to 6.8 on July 1. Talks were continuing last night.