Speaker Melissa Mark-Viverito and the City Council’s top municipal ID boosters applied for their IDs Thursday – even as New Yorkers continued to face long waits to apply for the cards.

The website where residents can make an appointment to get an ID was back up and running Thursday after crashing on its first day in operation – but as of mid-afternoon, the earliest available appointment at the central Brooklyn Public Library was for March 4.

Mark-Viverito defended the program as she and five other Council members put in their paperwork at the library.

“This is a good challenge to have, when you have such an overwhelming demand,” she said, noting the inoperable website was quickly fixed. “As we go along, we learn the challenges, and we work along the way to resolve them.”

She said the city might open more enrollment centers to cut down on wait time, and that the troubles with the rollout were nothing like the botched enrollment process for Obamacare.

““That is really an unfair comparison,” Mark-Viverito said. “We’re talking about a temporary hiccup in a rollout that has been extremely positive.”

The cards, which any city resident can apply for, are intended to provide an official ID for undocumented immigrants, the homeless, transgender people, and other who struggle with government ID.

“For many years I’ve carried an ID that did not match my gender identity, and this impeded me from cashing checks, applying for different benefits, and going about my life,” said Phoenix Natasha Russell, a transgender Brooklyn woman who applied for a card alongside the pols Thursday. “This municipal ID…validates me as a New Yorker.”

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