Louisiana’s higher education institutions still have a slim chance of gaining some control over how much they charge for tuition and fees, but time is winding down.

After rejecting a similar proposal on Monday, the House voted Tuesday to negotiate with the Senate over the two chambers’ differences on House Bill 61 — just days before the session ends at 6 p.m. Thursday.

Tuition and fee control were among key priorities for colleges and universities heading into the session. It takes two-thirds of the House and Senate to increase tuition at Louisiana’s public colleges — the highest hurdle for any state.

The rejected proposed constitutional amendment sought to hand over that authority to the state Board of Regents.

The latest proposal would ask voters to decide whether the Legislature could raise tuition with a simple majority vote — rather than the two-thirds currently required — or delegate that authority to management boards.

“This would still provide legislative oversight of raising tuition,” said Rep. Thomas Carmody, a Shreveport Republican who authored HB61.

Changing the way prices are set wouldn’t necessarily translate to higher costs for students immediately, higher education leaders have claimed. Some of the regional colleges have sought to lower their tuition to keep from pricing out some students and to grow enrollment. Also, the state GRAD Act remains in effect for two more years, which already allows schools to raise tuition 10 percent each year if they meet certain academic benchmarks.

The Legislature has sent to Gov. Bobby Jindal a separate bill that seeks to rein in the cost of Louisiana’s generous TOPS scholarship program by eliminating the automatic increases in award amounts when tuition goes up. That legislation was seen as key to giving schools control over tuition because of the link between the two.

Jindal has expressed concern over Senate Bill 48, but he has not outright said whether he will veto the bill.

But Carmody said he didn’t want his bill to be entirely dependent on Jindal signing off on a separate bill. The Senate had amended his measure to link the two.

“I do not want my constitutional amendment tied to a bill that could be vetoed,” he said. He argued for the bill to be sent to conference so the differences could be worked out.

In other action, the House gave final approval to a bill that will allow the higher education management boards to create new fees, including credit-hour fees, for varying programs over the next two years. The proposal, if signed by Jindal this year, would require action from the Legislature to extend beyond the 2016-2017 school year.

Follow Elizabeth Crisp on Twitter, @elizabethcrisp. For more coverage of Louisiana state government and politics, follow our Politics blog at http://blogs.theadvocate.com/politicsblog.