TALLAHASSEE — A panel of appeals court judges will hear oral arguments on Tuesday in the next phase of a high-profile and controversial lawsuit challenging a voucher-like scholarship program that helps poor children attend private school in Florida.

But the merits of the Florida Tax Credit Scholarship program won’t be argued just yet.

First to be resolved is whether the state’s largest teachers union and other plaintiffs even have the right to make their case that it’s unconstitutional.

The Florida Education Association and its allies want the First District Court of Appeals in Tallahassee to overturn a Leon County judge’s ruling from almost a year ago that tossed the lawsuit. Circuit Judge George Reynolds III ruled that the plaintiffs didn’t have legal standing to bring the case.

The FEA appealed last summer because it wants its day in court — despite mounting public pressure from scholarship supporters who want the union to “drop the suit.”

“We, as an organization, believe the Florida Legislature has overstepped their bounds and created an unconstitutional situation,” FEA President Joanne McCall said Monday. “There should be checks and balance, and we should have the right to challenge the Legislature when we believe that they’ve done something unconstitutional.”

At the root of the lawsuit, the FEA argues the scholarship program diverts would-be tax dollars away from public education to private schools. The union says that means the state isn’t fulfilling its constitutional duty of providing “a uniform, efficient, safe, secure, and high quality system of free public schools” to all.

Under the scholarship program, businesses can get dollar-for-dollar tax credits — as much as $447 million this year, growing to $560 million in 2016-17 — for donating to one of two organizations that fund the scholarships. Nearly all of the scholarship money is facilitated by Jacksonville-based Step Up For Students.

The donations are used to provide scholarships of $5,677 to more than 78,000 children, so their families can afford to send them to private schools that might provide them a better environment than traditional public schools, which serve 2.7 million children.

Supporters of the scholarship program have waged a months-long marketing campaign against the FEA under the slogan “drop the suit,” but McCall said the union has “absolutely not” considered backing down.

Among the supporters’ efforts, Washington, D.C.-based American Federation for Children spent $1 million in January to put on a massive rally in Tallahassee — on a school day — that featured thousands of parents and children from across the state and special guest, Martin Luther King III. Video and speeches from that event were later used for TV and online ads paid for by the “Save Our Scholarships” Coalition.

More recently, proponents have been heralding the scholarship program and criticizing the teachers’ union, during speaking engagements before influential statewide groups.

Tampa businessman John Kirtley — who helped lawmakers create the tax-credit scholarship in 2001 and who now serves as chairman of Step Up for Students — highlighted the lawsuit during a speech before the Economic Club of Florida last month in Tallahassee.

And last week in Miami, the lawsuit also came up during a panel discussion on educational choice that was sponsored by the James Madison Institute, a Tallahassee-based free market think tank that supports school choice policies.

Julio Fuentes, president of both Hispanic CREO and the Florida State Hispanic Chamber of Commerce, said during the Miami luncheon that the teachers’ lawsuit presents “a clear threat upon us right now.”

“We’ve been fighting it; the one good thing is that we’ve been winning in the court of public opinion,” Fuentes said, citing the proponents’ efforts to “fire up our base.”

Another example: Three hours before Tuesday’s hearing, the Florida African American Ministers Alliance for Parental Choice — comprised of more than 100 black ministers — has a press conference planned in Tallahassee to call on the NAACP to withdraw from the lawsuit.

Although Florida’s NAACP chapter has sided with the FEA, many black and Hispanic community and religious leaders in the state support the scholarship program.

It predominantly helps minority students, and almost 70 percent of the participating private schools are religious. About 38 percent of children receiving scholarships are Hispanic and another 30 percent are African-American.

More than a quarter of the students — almost 20,900 — live in Miami-Dade County, and another 9,600 students live in Broward, Palm Beach or Monroe counties. About 11 percent of the students — approximately 8,600 — live in the Tampa Bay area.

Proponents caution that if the scholarship program is dismantled, 80,000 children will be booted from private schools that work for them and they’ll potentially burden Florida’s public education system, which couldn’t accommodate such an abrupt influx of kids.

McCall shrugs off the supporters’ campaign.

“I’m not sure what the hoopla is about,” she said. “If they’re so confident they’ll win, they’ll let the courts decide.”

The Florida School Boards Association initially joined the FEA in the suit but withdrew last spring, when it decided not to appeal Reynolds’ ruling. But the FSBA was nonetheless penalized for its participation. The group drew the ire of conservative lawmakers this spring who approved funding and policy changes that favored a rival organization of individual school board members, which didn’t like the FSBA taking part in the lawsuit.