Yes, this suggestion seems preposterous at first, but I'd commend you to consider the following questions: (1) Should anyone put it past Anthony Weiner to chart an accelerated course to reclaiming the power he so clearly craves? (2) This saga has witnessed countless mind-blowing turns (Andrew Breitbart hijacking Weiner's press conference comes to mind), why not one more? (3) Could he win? Against that backdrop, take two: Could Anthony Weiner resign, then run for re-election?
To the extent that Weiner has sinned against his wife and his marriage vows, that is a private matter. To the extent that his behavior has brought the House into disrepute, that is a public sin. But—barring the revelation of new and more disturbing facts—the sin in this case hardly warrants expulsion. Unlike, say, members who accept bribes, Weiner's behavior causes eye-rolling, not an actual loss of faith in the institution's ability to govern fairly. For bringing the House into (some) disrepute, Weiner may deserve a censure, but his behavior can hardly be said to warrant expulsion.
Weiner's worst public sin is the lies he told. For those, he should do penance and seek the forgiveness of his constituents. And the best way for him to do that is to put his fate in their hands. He should offer his resignation. The House should accept it. And he should, if he still desires to be in Congress, run for his seat. He will have to humble himself; he will have to explain himself; and he will have to ask for the public's trust to be placed in him anew. And if his constituents do re-elect him, it will be because they've decided, with all of the facts on the table, that he is worthy of their trust. It will be a moment of political redemption, a vote of confidence in him from his real bosses, the people of his district. And there the matter should be left to rest.
UPDATE - Bill Clinton is reportedly still "livid" with Anthony Weiner. Does. Not. Compute:
The Clintons, the sources said, and their extended world, are furious and want no contact with Weiner. But they are deeply supportive and protective of Abedin, whom Clinton called a “second” daughter when he officiated her wedding. “They are livid,” said one source affiliated with Hillary Clinton.
UPDATE II - CNN's Wolf Blitzer is thinking similar things.