Senators agreed Thursday to begin debating a bipartisan proposal to renew federal unemployment benefits for the long-term jobless that would allow for retroactive payments to go to more than 2 million Americans whose benefits started expiring in late December.

Sens. Robert Menendez (D-N.J.), Jack Reed (D-R.I.) and Dean Heller (R-Nev.). Reed and Heller are lead sponsors of the bipartisan unemployment insurance deal. (AP)

Senators voted 65 to 34 to proceed to debate on the bill, ensuring it will pass easily at some point next week.

All 55 members of the Senate Democratic caucus voted to proceed as well as 10 Republicans -- Sens. Kelly Ayotte (R-N.H.), Dan Coats (R-Ind.), Susan Collins (R-Maine), Bob Corker (R-Tenn.), Dean Heller (R-Nev.), Ron Johnson (R-Wis.), Mark Kirk (R-Ill.), Lisa Murkowski (R-Alaska), Rob Portman (R-Ohio) and Patrick Toomey (R-Pa.).

Heller and Sen. Jack Reed (D-R.I.) led a coalition of ten senators, evenly divided among Democrats and Republicans, in weeks of careful talks that resulted in the announcement of a pact two weeks ago.

But its outcome in the House remains uncertain, as Speaker John A. Boehner (R-Ohio) has opposed previous Senate plans as insufficient in providing offsetting cuts and has highlighted the concerns of state unemployment officials who've warned that implementing the new agreement might prove too onerous for some states.

The bill would effectively restart a key aid program for long-term unemployed workers whose jobless benefits went beyond state limits, which are about 26 weeks with some variation for each state.

The roughly $10 billion cost of the renewed federal jobless benefits would be offset by extending fees on goods coming through U.S. Customs and a change to the way corporations contribute to pensions, the senators announced.

In addition, the legislation will include two revisions to the unemployment program, one of which will require more job training for long-term jobless workers in order to continue receiving insurance benefits. Also, the legislation includes a provision that eliminates state or federal unemployment benefits for laid-off workers whose gross income the previous year topped $1 million — which, according to federal estimates, represented 0.03 percent of all recipients.

Debate on the measure is expected to dominate the early part of next week in the Senate and then focus is expected to shift to a proposal to raise the federal minimum wage to $10.10.

Paul Kane contributed to this report.