As the New Orleans City Council prepares to hear passionate and probably lengthy arguments from both sides Thursday afternoon in the debate over whether to remove monuments honoring Confederate leaders and a white militia group from their pedestals throughout the city, a second member of the council has come out against the ordinance that would allow the removal.

In the meantime, Mayor Mitch Landrieu, who this summer started the process that could lead to the monuments’ removal, has left numerous questions about how the removal would proceed unanswered.

The council is considering an ordinance that would allow the removal of the statues of Gen. Robert E. Lee in Lee Circle, Gen. P.G.T. Beauregard at the entrance of City Park and Confederate President Jefferson Davis on Jefferson Davis Parkway, plus a monument to the role of the White League in the 1874 Battle of Liberty Place that stands on Iberville Street near the river.

Councilwoman LaToya Cantrell, who had called for removing at least one of those statues before the mayor did, said in a news release Wednesday that the administration-led process had been “thrust upon the city and the council from the top down after it was created by a small, select group of individuals.”

“There was no movement rising up to demand this action,” Cantrell said. “There was no willingness to take into account people’s outrage about other symbols of racism not included in this ordinance. There was no discussion on whether one or two of the selected monuments might be more offensive than others.”

Councilwoman Stacy Head said Tuesday that she felt the process was headed to a “foregone conclusion” and that she could not support what she described as a rushed and “flawed” process.

Neither Cantrell nor Head defended the monuments themselves. Both councilwomen, who each have clashed with the Landrieu administration in the past, instead argued that the mayor has attempted to force the matter on the city since first announcing his desire to remove the statues.

“It was determined to be necessary by leadership from the privilege of power. This is not fair,” Cantrell said of Landrieu’s initiative.

She also argued that the discussion has distracted attention from more important matters, such as crime, infrastructure problems, affordable housing and blight.

Cantrell was considered one of five council members likely to support the ordinance. Even before Landrieu officially called for the removal of the four statues, she had suggested removing the Jefferson Davis statue and renaming the street that bears his name. She spoke in support of Landrieu’s proposal when it was first introduced. Councilmen Jason Williams and Jared Brossett and Councilwoman Nadine Ramsey also spoke in favor when Landrieu first proposed the measure over the summer, and Councilman James Gray, who was absent at that meeting, had signed on as a co-sponsor.

Councilwoman Susan Guidry has not announced her position.

Meanwhile, the Landrieu administration has not responded to numerous questions about what will happen if the council votes to declare the monuments to be “nuisances” that should be taken down.

The Mayor’s Office said months ago that a private donor had offered to pay the estimated $144,000 it would cost to remove the statues. It said they would be stored in a city warehouse until new locations could be found for them.

City officials did not respond Wednesday to requests for further details.

Nor did they address Head’s suggestion that the administration already has selected a company to remove the statues. Head’s email did not provide specific information backing up that claim, but it mirrors concerns raised by groups opposed to the removal such as the Monumental Task Committee and Save Our Circle.

Some critics have suggested that selecting a contractor without an open process would run afoul of public bid laws.

The administration also has ignored questions about whether it has plans for where the statues might eventually end up. Many have speculated they could find their way to a museum or similar institution, but the administration has not said whether it has contacted any organizations that might be interested in taking them.

Follow Jeff Adelson on Twitter, @jadelson.