Updated 5:09 p.m. ET, 7/24
(CNN) - It didn't take long for the calls to come in for Anthony Weiner to withdraw from the New York City mayoral contest following his shocking admission Tuesday that he sent lusty messages more than a year after resigning from Congress for the same dubious habits.
But Weiner said Wednesday that his fate will ultimately be up to the voters.
"That's for the citizens to decide," he told reporters outside of his apartment.
"And you know I'm fine," he added. "I've got an amazing wife, and a child upstairs. I have a comfortable life. This is not about me, this is about the fact that the middle class has people struggling to make it in this city."
The editorial board of the New York Times urged Weiner to take his personal struggles "out of the race for mayor of New York City." The New York Post belittled him as "Carlos the Jerkel," a reference to Weiner's use of the online alias "Carlos Danger." And pundits wondered how someone who had shown such poor judgment was even in the race.
In an extraordinary news conference, Weiner and his wife, Huma Abedin, pleaded Tuesday for voters to forgive the embattled candidate, as his wife says she has forgiven him. Weiner also reminded the public that he warned at the beginning of his campaign in May that more photos and texts could emerge.
But the Times editorial board didn't buy it.
"That's ridiculous and speaks to a familiar but repellent pattern of misleading and evasion," the board wrote. "It's up to Mr. Weiner if he wants to keep running, to count on voters to forgive and forget and hand him the keys to City Hall. But he has already disqualified himself."
PHOTOS: Weiner addresses lewd exhanges
His press conference remarks came hours after screenshots of sexually explicit conversations and photographs appeared on a gossip website that alleged the communications were between Weiner and a young woman last summer, just as Weiner and his wife were beginning to reemerge from their private lives for public interviews.
"Some of these things happened before my resignation, some happened after," Weiner said at the hastily organized press conference in New York.
Another prominent newspaper, the New York Daily News, also released a scathing editorial, listing lie after lie by the former congressman.
"He is not fit to lead America's premier city," stated the editorial, titled "Why Weiner must go". "Lacking the dignity and discipline that New York deserves in a mayor, Weiner must recognize that his demons have no place in City Hall."
Rupert Murdoch, who owns the New York Post, tweeted "Weiner almost tragic if not so funny. What a sicko. Should help city by just fading away."
Weiner argued Wednesday that his decision to run for mayor was "the right thing to do for the city," and voters have bigger issues on their minds than his personal mistakes.
"Look I know there are people who may well never consider voting for me because what's in my past. And even for those people I want them to hear about my ideas," he said. "At the end of the day citizens are more interested in the challenges they face in their lives than anything that I have done embarrassing in my past."
And as Weiner predicted, some of his opponents for the mayoral nomination also urged the contender to drop out.
"Enough is enough. I'm calling on Anthony to withdraw from this race – for the good of the city that I know he loves as much as all of us," tweeted Public Advocate Bill de Blasio. He also started an online petition urging others to call on Weiner to end his campaign.
Two other candidates, John Catsimatidis and Sal Albanese, tweeted similar pushes for Weiner to step aside.
Weiner's closest rival, City Council Speaker Christine Quinn, wrote in a statement that Weiner's candidacy had turned the mayoral race into a "circus."
"Being the Mayor of New York is serious business and it demands a serious leader. Instead we have seen a pattern of reckless behavior, consistently poor judgment, and difficulty with the truth," she wrote.
But Weiner has implied he plans to do anything but leave the contest in the weeks leading up to the Democratic primary election on September 10.
"You know there have been people since the moment I got in the race that didn't want me to run," he said Wednesday. "But a lot of people have been crying out for someone to talk about issues important to the middle class."
In a lengthy email to supporters later Wednesday, he declared: "New Yorkers don't quit, and I'll never quit on you."
Weiner resigned his House seat in 2011 after first lying about, then admitting to sending lewd photographs and images to multiple women. In the email to supporters, he said he "answered every question about these mistakes" before and after announcing his run for mayor this year, but expressed regret that he did not specify "when these exchanges happened."
Unlike his public resignation two years ago, Abedin spoke up for her husband Tuesday at the press conference, saying she has moved past her husband's addiction and urged others to do the same.
"What I want to say is I love him, I have forgiven him, I believe in him, and as I have said from the beginning, we are moving forward," said Abedin, a longtime senior adviser to Hillary Clinton, adding that Weiner had made some "horrible mistakes, both before he resigned from Congress, and after."
John Avlon, senior political columnist for The Daily Beast and CNN contributor, argued Abedin is simply following the model set by Hillary Clinton.
"Part of the Clinton playbook is success heals all wounds. Let's just win and all this tawdry mess will be in the rearview mirror," he said on CNN's "New Day."
Weiner argued he had changed.
"This behavior is behind me. I've apologized to Huma and am grateful that she has worked through these issues with me and for her forgiveness," he said Tuesday.
But his words were not convincing for the New York chapter of the National Organization for Woman, which quickly called on Weiner to withdraw from the race following his press conference.
"As if we didn't already have enough evidence of Anthony Weiner's utter lack of judgment, impulse control and honesty, these latest revelations show the degree to which his candidacy distracts us from the important business of choosing the next leader of New York City," Sonia Ossorio, the president of the group, wrote in a statement.
The chat messages purporting to be from Weiner were published on the website TheDirty.com. The post cited a "solid" source alleging Weiner engaged in lewd online conversations with her, and reproduced lengthy chats that were sexual in nature. A blurred photo of what alleges to be Weiner's crotch also appeared on the site.
"I just want people to really know he's lying when he acts like he has changed," the unnamed woman, 22, told TheDirty.
In his email to supporters Wednesday, Weiner said the exchange was "a terrible mistake that I unfortunately returned to during a rough time in our marriage."
Former New York Gov. Eliot Spitzer, another disgraced politician trying to make a comeback, said Weiner's new controversy is between him and his wife.
"Look I'm running my own campaign and I have been since the day I got into this and so I have no comment about other than I'm gonna be talking to the voters about what I have done, what my plans are and will be going forward with my premise," he said Wednesday morning at a campaign stop, according to CNN affiliate NY1.
A source close to Spitzer told CNN the candidate is not overly concerned with the Weiner controversy.
"We think that voters have already separated Spitzer and Weiner in their minds," the source said, pointing to numbers in a recent Quinnipiac poll, adding the latest controversy provides an opportunity for Spitzer to continue to make his "individual" case.
Spitzer resigned as New York governor in 2008 after admitting to paying prostitutes for sex.
The verdict is still out on whether Weiner will survive the latest firestorm. Polls taken over the past several weeks have shown Weiner either slightly ahead of his closest rival for the Democratic mayoral nomination, City Council Speaker Christine Quinn, or trailing her in second place.
"He's been campaigning asking for a second chance. Now today he's asking for a third chance," Avlon said Wednesday morning. "That's fundamentally different in what the voters are being asked."
Ana Navarro, a Republican strategist and CNN commentator, said Weiner's latest admission will put him even farther under water with women voters.
"I don't claim to be a thermometer for the women vote, but I can tell you it'd be hard for me to vote for a guy who's now made his wife endure this kind of public humiliation," she said.
The calls for Weiner to step down were familiar refrains from Weiner's first scandal in 2011, when a tsunami of criticism engulfed Weiner, with few of his fellow Democrats coming to his side. After a few weeks resisting such calls, he ultimately resigned while confessing to the indiscretions.
In the run-up to his mayoral bid, which he launched in May, he said more photos could emerge.
"If reporters want to go and try to find more, I can't say they're not going to be able to find another picture, find another person who may want to come out on their own," he told RNN Television. "But I'm not going to contribute to that. The basics of the story are not going to change. It's behind me. It was a huge mistake."