Nyhan sees little reason to think so:

[W]hile Obama will have increased leverage in the upcoming “fiscal cliff” scenario, there’s little reason to think the upward trend in legislative polarization will relent any time soon, or that Obama can magically change public opinion from the bully pulpit or force Congress to act through outside pressure. Similarly, it’s not clear that a president’s re-election creates especially strong incentives for the opposition party to start compromising. It’s true, for instance, that Bill Clinton cut a budget deal with Republicans in 1997, but he was also impeached in 1998. Similarly, George W. Bush faced far more relentless and effective opposition from Democrats in Congress during his second term than his first. Despite John Kerry’s loss, Democrats killed Bush’s proposal to add private accounts to Social Security in the 109th Congress and subsequently won a landslide victory in the 2006 midterm elections.

Sprung counters:

[T]he points that Nyhan concedes — that  a reelected Obama would have the whip hand in fiscal cliff negotiations, and that Clinton cut a budget deal (largely reflecting his priorities) after his reelection –  go a long way toward making Obama's argument for him. "Breaking the fever" is not primarily, or initially, about about producing comity between the parties; it's about changing the opposition's incentives. Clinton's reelection did do that; the fact that he later handed the Republicans a sword to gore him in the person of Monica Lewinsky does not negate the leverage he won or the relatively rational compromises he was able to strike with a GOP Congress — yielding balanced budgets that Gingrich boasted about in the GOP primaries as if he'd been Clinton's right-hand man.