Senate Finance Committee Chairman Jack Donahue is proposing to raise the minimum grade point average and ACT score required to get a TOPS award for future students.
Gov. Bobby Jindal's privatization deal for the LSU hospital in Lafayette was running $6 million over budget by April's end with two months remaining in the fiscal year.
Opponents say the new restrictions are medically unnecessary and are designed to limit women's access to abortion.
Appropriations Committee Chairman Jim Fannin, who handles the budget bill, began the debate by talking of the state's ongoing budget problems, saying balancing the spending plans is always difficult.
The tuition program will remain untouched for now, but state lawmakers could get special gun priviledges.