Gov. Bruce Rauner said late Friday he’s found a compromise on his own snag involving tax-credit scholarships for private schools that was holding up funding for public school districts statewide.

A Democratic legislator who shared the Republican governor’s concerns about the scholarships said procedural changes have been made to the rules governing which privately managed schools could accept the publicly-funded credits, expanding the list to include several Chicago-based Catholic schools.

The fix essentially gives private schools more time to become recognized by the Illinois State Board of Education, instead of limiting the list to schools that already underwent the process and accompanying school visit, and it smooths the way for public schools to be funded.

Earlier this month, Rauner abruptly filed an amendatory veto that halted the release of money to public school districts agreed upon last fall in a historic school funding bill. The legislation ultimately contained the benefit for private schools; though Rauner had agreed to it, he later determined it left out too many private schools. ISBE warned that the halt could delay payments based on the new funding formula to the state’s 800-plus districts.

“The compromise is in place now,” Rauner spokeswoman Rachel Bold said Friday. “The General Assembly can now either choose to override the [amendatory veto] or pass another bill with the same language.”

But the “compromise” as the governor’s press release called it isn’t yet a guarantee. The full General Assembly, which goes into session next week, still would have to vote on a legislative fix, and Rauner still would have to sign off on the results.

“We will decide as a caucus what to do on Tuesday,” said Downstate Sen. Andy Manar, the Democratic architect of the historic funding measure. “I’ll do whatever our caucus decides as a group.”

Earlier this week, an ally of House Speaker Michael Madigan introduced a resolution with generally the same administrative solution that Rauner has agreed to.

Another legislator, state Rep. La Shawn Ford, D-Chicago, had called for the fixes, saying a number of good schools such as Hales Franciscan High School in Chicago, had been left out of the five-year pilot program that grants $75 million in tax credits to donors of scholarships for low -income students.

Now a group of between 30 and 40 schools that had applied for ISBE recognition when the funding agreement passed but hadn’t yet achieved it, will have a chance to qualify for this round of scholarships, he said. Another 250 schools considered “registered” with the state board could apply for the more vigorous “recognition” in time, he said. The state board also promised to publish the names of the qualifying schools as they are approved so families can see them, instead of on an annual basis.

“I argued this even before the actual school funding bill passed, I knew we had problems with the actual tax credit” scholarships,” that found their way in, he said. “If the Legislature had done it right and had public hearings, this problem wouldn’t have occurred. Because it acted irresponsibly, these are the consequences.”

The Illinois State Board of Education also will publish a list of schools whose recognition status is pending, so students interested in attending can get in line for scholarships to those schools. The money will be awarded starting Feb. 1 on a first-come first-served basis, so the scholarship granting organization Empower Illinois is urging families to apply even if their school isn’t on the final list to reserve their place in line.

“Please be aware that no funds will be distributed for a student’s enrollment unless the school becomes recognized,” the group told parents.