Edwards spokesman Richard Carbo said Monday the governor believes the Senate "has passed an acceptable compromise."
Edwards wanted to use nearly $120 million from the state's "rainy day" fund to help fill the gap, other reserves and $60 million in cuts.
The House budget-rebalancing proposal would use $75 million from the rainy day account.
Edwards and senators say the $115 million in cuts required under the House proposal would be too deep, damaging security in state prisons, the rural hospitals and the education department.
The Senate rewrote the budget proposal to cut around $80 million and use $99 million in rainy day money.
Time is running short to reach a deal. The special session must end Wednesday.