I can't see that happening in 2012. The conditions simply aren't right. At best the Democrats hope to hold the White House and a slim majority in the Senate; they have no hope of taking back the House, let alone getting a filibuster-proof majority in the Senate. And politically it just won't be possible to convince voters that in a political climate that still sees the deficit as a major priority in the middle of recession, the government should create an even more ambitious ("radical socialist" if you're a Republican) plan to replace one that was found unconstitutional. (Yes, legally speaking that doesn't follow, as even virtually all of the law professors championing the anti-Obamacare cause acknowledge that single-payer would be constitutional, but voters won't see it that way.) Nor could you get a Democratic caucus to unite solidly behind any such proposal anyway -- one of the reasons they got such good party discipline on Obamacare is that the insurance companies were on board rather than fighting it tooth and nail.
Long term, yes, the Democratic Party will conclude that the only path the Court has left open is a more government-based system. My guess is that in 2016, the Democratic primary race will involve various of "Medicare for all," and that the eventual consensus will be an incremental approach of gradually lowering the eligibility age for Medicare, possibly with an opt-out to preserve "choice."
