The National Republican Congressional Committee issued a statement needling Democrats and asking them to "explain why Congressman Weiner's actions never aroused any suspicion, and why they rushed to his defense."
New York State Republican Party Chairman Ed Cox called on Weiner to resign, declaring, "His actions are at best despicable and at worst illegal."
Weiner repeatedly said Monday he would not resign his 9th district seat, but he did not explicitly say he would seek re-election.
Asked about the electoral consequences of his actions, Weiner said the last thing he's thinking about is "next year's election or the election after that."
"I'm going to work very hard to win back [voters'] trust," he said. "Nothing about this should reflect in any way on my official duties or my oath of office."
While the political boundaries could change because of redistricting, the 9th district is currently Democratic-leaning. It includes parts of Queens and Brooklyn. Despite a couple of close calls last fall, Democrats largely dominate New York City's federal races, with the exception of GOP Rep. Peter King's 3rd district seat.
Given the scandal's daily treatment in New York media — particularly tabloids like the New York Post — it is unlikely to retreat from the public's mind.
"The Post is widely read in New York City and people are not going to forget this," former Democratic operative Curtis Ellis said before Weiner's press conference. "It's going to be very hard to take this guy seriously if he runs for mayor."
He continued: "This now puts Anthony Weiner officially in the category of, 'Oh, he's one of those guys.'"
Nick Langworthy, the Erie County Republican chairman and the former district director for Lee, said constant scandals do "desensitize people." He added: "The bar is set very low right now in what is expected of public officials."
Paul Singer contributed to this report.
This article updates the print version to include comments from Sen. Charles Schumer.
Senate Minority Leader Mitch McConnell, R-Ky., carries a musket on stage as he speaks during the American Conservative Union's Conservative Political Action Conference (CPAC) at National Harbor, Md., on Thursday March 6, 2014.