The legislators had approved the measure by a 17-to-1 vote in April.
Last year, legislators approved a 15 percent income tax increase that was supposed to be temporary.
Legislators approved shipping more than 2,000 prisoners out of state.
The legislators narrowly approved the change, in a vote of 10 to 8, on Tuesday night.
The legislators must approve a final version of the budget by Dec. 27.
And with congressional elections set for July, few believe that legislators will approve the controversial changes.
Legislators have already approved the betting site, but the other provisions require state and county legislation.
Legislators also approved raising the minimum dropout age to 18 during the special session.
Even as legislators approved the measure, which most said was likely to be enacted, they expressed some ambivalence.
The move is part of a constitutional reform package that legislators approved at an unexpected session on Sunday.