Parliamentary procedure, it seems, can trip you up even when you know exactly what you want to vote for.

On Saturday, newly elected Alexandria City Council members Allison Silberberg and John Taylor Chapman thought that they were defending the need for working families in a new affordable housing complex to be able to park for free in the building’s garage, the first important vote of their term. Instead, they accidentally — and temporarily — voted against 78 new affordable apartments in the increasingly expensive inner suburb.

During a lunch break, as Chapman explained the vote he thought he had cast to a reporter, Mayor William D. Euille (D), his political mentor, approached.

“You realize you voted against affordable housing?” the mayor said to Chapman. “Did you really want to do that?

“If you want a reconsideration vote, go talk to the city attorney now,” Euille said.

Chapman, who was raised in low-income housing himself, appeared stricken.

He immediately said that he wants more affordable housing and considered AHC Inc.’s proposal a good one. He and Silberberg had lost a vote on an amendment that would have required free parking in the building; their “no” votes on the main motion to approve the project, which the rest of the council supported, were what concerned Euille.

By that time, Silberberg had already conferred with the city attorney. She called herself a “lifelong, fierce advocate of affordable housing” but worried that the families who could pay $1,200 per month for a one-bedroom or $1,650 per month for a two-bedroom unit might not be able to afford an additional $35 or $40 per month for parking.

“I don’t know all the ins and outs of parliamentary procedure, but that can be learned,” she said. “We need housing for people who are teachers and city staff in Alexandria.”

Requiring the developer to provide free parking, Euille said, could endanger the developer’s financing and tax credits, risking the project.

The council voted again a few hours later, agreeing unanimously to approve the $250 million project. The city will loan AHC $2.5 million and donate land at Route 1 and East Reed Avenue. Other council members termed the project “an incredible bargain.”

The project is scheduled to open by 2015. By that time, council members noted, there will be a bus rapid-transit stop just outside its doors, a new Metro station may be under construction at nearby Potomac Yard, and an Arlington County streetcar line will be running a few blocks north.