TALLAHASSEE — Efforts to ban or significantly limit abortion in Florida have long been a fractious endeavor: Though legislators have filed bills nearly every year in the last decade seeking to restrict or prohibit the procedure, they have been met with at best limited success.

This year, with a new governor and three new conservative justices he’s appointed to the Florida Supreme Court, some lawmakers are hoping a proposal to significantly limit when abortions can be done might help sway colleagues into supporting the bill.

House Bill 235 and Senate Bill 792, filed by Rep. Mike Hill of Pensacola and Sen. Dennis Baxley of Ocala — both Republicans — would ban abortions once a fetal heartbeat can be detected via vaginal ultrasound, which can be as early as six weeks. The proposed “heartbeat” bill has been taken up — and in some cases passed — in a handful of other states, though those that have become law have drawn legal challenges, notably North Dakota’s, which the U.S. Supreme Court struck down in 2015.

Hill and Baxley say that the new conservative justices at the state and federal level might make the courts more friendly to reconsidering the existing standards permitting abortion — and that a legal challenge is indeed necessary to change state and federal law. It is another example of how lawmakers are increasingly looking to the courts to help advance their policy agenda, and how a friendlier bench on the high court has emboldened them to resolve perennial issues in their favor.

“It requires being challenged, if it’s to pass, if it’s to change the big picture,” said Baxley, adding: “I don’t think it’ll have a problem attracting one.”

Abortions can currently be performed in Florida up to 24 weeks, in accordance with state and federal law, including the U.S. Supreme Court Roe v. Wade decision in 1973 that prohibits an “undue burden” on abortions before a fetus is viable.

Gov. Ron DeSantis, when campaigning, said he would support and sign a fetal heartbeat bill if it crossed his desk. But to get there, the bill would have to clear the long-running legislative hesitation to tackle the issue. The bill is not a top legislative priority and though it has been assigned to committees, both bills are still awaiting a hearing.

Though some legislators have tried for several years in Tallahassee to either ban or restrict abortion, significant limitations on when abortions can be performed during a pregnancy have failed in the past. Some bills filed in recent years to ban abortions outright have failed to clear legislative committees or be heard at all.

Most of the bills that have passed on abortion have instituted restrictions on what is required to obtain or perform the procedure. A 2016 bill that would have instituted waiting periods before obtaining abortions, for example, almost immediately drew a tangled, ongoing challenge.

And even if conservative justices might seem more inclined to take up a banner issue like abortion, they may be reluctant to so dramatically change existing precedent immediately.

“On an intensely political issue like abortion, I think it’s not likely most judges want to look like they completely overhauled the law without some kind of buildup,” said Florida State University professor Mary Ziegler, who has written on reproductive law. She added that “overturning everything quickly” might be perceived as a threat to the “institutional legitimacy of the court” and make them look more partisan.

“There’s obviously always been an appetite for bills like this because many abortion opponents see abortion as violent and homicide,” she added. “Whether you can have that much social change in that short a time is still a pretty open question.”

But pro-choice opponents to the bill are nevertheless alarmed, and have taken particular issue with the fact that many women do not learn they are pregnant that early. They say such an early bar for performing abortions would amount to a wholesale ban on the procedure.

“In terms of this year, yes, there is definitely a heightened concern,” said Laura Goodhue, executive director of the Florida Alliance of Planned Parenthood Affiliates. “This is a bill that would take a woman’s options away before she even knows she’s pregnant — we do see this as one of the most extreme attempts. … There’s definitely clear precedent that this is unconstitutional.”

A less aggressive abortion bill filed this year, Senate Bill 558, would ban abortions after 20 weeks, said Sen. Joe Gruters, R-Sarasota, who filed the legislation. But that bill has no House sponsor, which likely dooms its chances of passage without a companion in the opposite chamber.

“A lot of times people want the all-or-nothing deal, in politics today,” Gruters said, noting he’d vote for the heartbeat bill if it came before him. “I just don’t think it’s going to pass.”

He said he was hopeful that the new judicial landscape might persuade lawmakers who had otherwise considered bills on abortion to be dead on arrival to support some kind of legislation, but cast his legislation as a more incremental and more likely to be successful approach, citing the Legislature’s recent reticence to pass aggressive limitations.

Gruters, who chairs the state Republican Party, also noted that controversial issues like abortion, which he said are not broadly top priorities for voters, make it “hard to justify all the members take some of these difficult votes.”

“I don’t know if there’s a strong push to have any of these bills heard this cycle.”

But Baxley, the heartbeat bill’s sponsor, said he was still hoping fellow lawmakers would consider it.

“People didn’t want to talk about it, I understand that. It’s hard to ask your fellow members when things are very divisive in their community to vote for something like this, but at the same time, that’s what leading is all about.”