Senate Finance Co-Chairman Sen. Chuck Colgan made the comments Monday following Democratic Sen. Phil Puckett's resignation.
His position largely mirrors what GOP lawmakers have pushed for. But Colgan said he "would love" some assurances that Medicaid expansion would pass during a special session, which would be unlikely given the strong Republican majority in the House of Delegates.
Puckett's departure has given Republicans a one-seat majority in the Virginia Senate. It may break a stalemate over the state budget that's being held up because of partisan disagreements on Medicaid expansion.
Lawmakers are set to meet later Monday to discuss possible new action related to passing a state budget.