“Families and students who rely on federal student aid need to know that Congress sides with them and not with the big banks,” Senator Tom Harkin, Democrat of Iowa and chairman of the Education Committee, said at a news conference on Thursday. “The federal government has been subsidizing these banks and wasting taxpayer money for far too long. It’s time to end it.”

Private banks had lobbied fiercely against the bill, which would cut off a longtime stream of revenue. Even on Thursday, lobbyists for the private lenders made a last-ditch effort to stop Democrats from adding it to the budget package.

House Democrats predicted that packaging the two proposals in an expedited budget reconciliation bill would help them secure the needed votes on health care because the financial aid bill is popular. In September, the House adopted that bill, the Student Aid and Fiscal Responsibility Act, by a vote of 253 to 171.

Senate Democrats said that they could lose some votes as a result of the packaging, but that they did not believe it would swing the outcome. Senate Democrats nominally control 59 votes, and need only 50 to approve the reconciliation measure, because Vice President Joseph R. Biden Jr. would break a tie.

Some Democrats in the Senate, where the private student loan industry has strong allies, had resisted tying the two bills together. But federal education officials warned on Thursday that if Congress failed to act, millions of students might see their Pell grants cut by 60 percent.