They said their timeline would resolve the case as quickly as possible. U.S. District Judge Myron Thompson agreed extra time is needed and indicated he would go along with the timeline since it was endorsed by both sides.
"It's up to you all," Thompson told the lawyers during a hearing.
The suit challenges a portion of the new law that requires doctors at abortion clinics to have approval to admit patients to nearby hospitals. The law was supposed to take effect July 1, but the plaintiffs sued, saying it would close three of Alabama's five licensed abortion clinics because the doctors can't get those privileges.
The suit prompted Thompson to temporarily stop the law from taking effect. His order had been due to expire Aug. 15 until both sides sought more time.
The Republican-controlled Legislature passed the law in April, with most Republicans voting for it and most Democrats voting against it. Republican legislative leaders have repeatedly pointed to the law as one of their major accomplishments of the 2013 session.
Proponents say it will provide safer abortions for women, while opponents say it will make it harder for women to choose to have one.
The timeline laid out by both sides calls for the judge to get the final legal arguments on the effect of the law on Jan. 31, 2014. He could rule then or schedule a trial, which attorneys said could result in a ruling before the party primaries on June 3, 2014, and certainly before the general election on Nov. 4, 2014.
That would put the abortion law in the news during the campaign season.
State Republican Party Chairman Bill Armistead said he doesn't expect it to have a major impact on the election because voters' views on abortion are already fixed. Armistead, a former state senator, said he doesn't expect Democratic legislators to make it an issue because it would backfire in a red state.
"Alabamians are pro-life and they want to protect the life of everyone," he said.
State Democratic Party Chair Nancy Worley said a well-publicized trial could bring out women voters who are concerned about losing a right. "You can be anti-abortion and pro-choice at the same time," she said.
Democratic state Rep. John Rogers of Birmingham, who voted against the law, said a ruling during the campaign would be a gift for Democrats, who are trying to recruit lots of female legislative candidates.
"Women are concerned about their rights being suppressed. This is our key to breaking the supermajority that Republicans have," he said.