Having had almost two full terms now, Bobby Jindal will not be on the ballot when voters elect a new governor next year. But two potential contenders for the job, from different parties, have in different words suggested that they’d like to change things he did.

Both will find it difficult, particularly with some of Jindal’s most significant legacies, a structurally unbalanced budget and a privatized system of public hospitals around the state.

Those big issues would pose big problems for either John Bel Edwards or David Vitter, the two candidates who have this summer outlined their goals in separate appearances at the Press Club of Baton Rouge.

They differ on many issues: Vitter is a two-term U.S. senator, a Republican from Metairie. Edwards is a two-term state representative from Amite and leader of the state House Democrats.

Edwards opposed the charity hospital privatization and was harshly critical of the process — including the LSU Board of Supervisors approving hugely important financial contracts with blank pages to be filled in later.

Vitter favored the end of the old charity hospital system, but he said that such a major change would involve adjustments over time in the public-private partnerships.

What both made clear is that there is no going back: Edwards said that’s not practical with thousands of workers having been laid off from the state.

If Vitter generally favors the new system, he or any other governor would nevertheless have to address one of Edwards’ criticisms of it: Having established public-private partnerships with some private hospitals in each region of the state, those hospitals’ competitors “are providing more care with less reimbursement.”

If Edwards studded his talk with Jindal’s name, and linked it often with Vitter’s, the senator did not mention the governor by name but explicitly criticized the “sewing yarn and Scotch tape” used to put the Jindal budgets together.

Spending for highways and infrastructure, and for education, has suffered, Vitter said. “In the area of higher education, we need to stabilize the system,” he added.

Both candidates talked in general terms about ending various exemptions from existing taxes.

Vitter limited himself to the observation that a lower tax rate could be funded with curtailing some tax exemptions. “I’m willing to look at everything,” he said.

Many exemptions for specific businesses may not be providing the benefits promised, or may be too expensive, Edwards said, but the Democrat explicitly ruled out the main sources of state money: “We are not going to have revenue-raising measures with respect to income tax and sales tax in the near future,” he said.

It’s early yet in the governor’s race, more than a year way from the Oct. 24 primary election. It’s reasonable enough that the candidates have not refined their presentations just yet, but the legacies of the Jindal years will be difficult to change, even for two candidates who are not political friends of the governor.