Asked about the bill now being considered, a spokeswoman for Mr. Edwards said the governor “doesn’t often weigh in on legislation that hasn’t made it to his desk.”

Although lawmakers in conservative states have advanced a barrage of measures intended to restrict access to abortion, including the prospect of criminal charges for providers, pursuing prosecutions against those who obtain the abortions has divided anti-abortion activists.

While campaigning for president in 2016, Donald J. Trump drew immediate blowback after he said patients who seek abortions should be subject to “some form of punishment.” He walked back his statement, saying later, “The woman is a victim in this case, as is the life in her womb.”

Louisiana is one of roughly a dozen states with a so-called trigger law, which would quickly make abortion unlawful if the Supreme Court overturns the constitutional right to an abortion. A challenge to a Mississippi abortion law has paved the way for the court to reconsider Roe v. Wade, the 1973 landmark decision establishing that right.

Still, proponents of the new bill in Louisiana argue that the trigger law is not enough. If passed, the bill would immediately ban abortion in the state, even before the Supreme Court issues its final decision. The bill would also enable the Legislature to ignore court rulings it disagrees with.

“Louisiana has already defied federal law by legalizing medical marijuana,” said Danny McCormick, the Republican representative who sponsored the bill. “If more than 15 states can defy the federal government over marijuana, we can do it to save the lives of innocent babies.”

Critics said — and even some supporters acknowledged — that the legislation, if passed, would likely be thwarted by the courts. Even so, detractors argued that the bill was reckless and stood to have devastating implications.

“It sets a precedent that could undermine our very system of government,” Gwyneth O’Neill, a lawyer who spoke against the bill, said during a hearing on Wednesday. “This bill is blatantly unconstitutional in many different ways.”