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After hitting snags earlier this week, key senators appear to be close to a deal to extend unemployment benefits for the long-term jobless through November.

A Senate Democratic leadership source told NBC News Thursday that the agreement would extend the jobless aid but limit how long states are eligible for federal benefits for their long-term unemployed.

The potential deal would extend some spending cuts mandated by budget sequestration for a year in order to pay for the extension. The cost of continuing the benefits for over 1 million unemployed Americans for most of 2014 is about $18 billion.

The proposal would also put some limits on people who receive both unemployment and Social Security disability benefits at the same time, saving an additional $1 billion.

The compromise plan would also cut the number of weeks that states are eligible for benefit payments from the federal government by 16 weeks -- reducing the total eligibility for benefits from 73 to 57 weeks.

Sens. Jack Reed, D-R.I., and Dean Heller, R-Nev., are the lead negotiators on the proposal, and some details were still being discussed Thursday afternoon. It's still not clear if enough Republicans would back the proposal to keep it from failing to overcome a filibuster.

On Wednesday, key Republican negotiators said they would not vote to advance the jobless bill further if backers did not find a way to offset the program's cost.

The Senate could hold procedural votes related to the proposal as early as Thursday afternoon.