Pretty much every presidential candidate in the last couple of decades has said that he was going to bring Republicans and Democrats together and end the partisan bickering in Washington that Americans so dislike. Bill Clinton said he would. George W. Bush said he would. Barack Obama said he would. All of them failed, and the one that tried hardest to do it—Obama—had a harder time than any of them. Despite the partisanship of their eras, both Clinton and Bush had significant pieces of legislation they passed with cross-party support, like Clinton's welfare reform and Bush's No Child Left Behind. But everything important Obama did was accomplished despite unified resistance from Republicans.
Conservatives might argue that the reason is that Obama is a uniquely partisan and vicious president, so cruel to Republicans that he's impossible to work with. But the real reason, as anyone who has been paying attention the last four years knows, is that Republicans made a decision upon his election that they would oppose anything and everything he wanted to do, and they've worked hard to make sure that their opposition is unanimous. After the 2010 election, in which a passel of Tea Party extremists was elected, whether or not to oppose Obama ceased to even be a question; the only question was whether they'd burn down the government to do so.
One unusual feature of this campaign has been that Mitt Romney hasn't said he's going to bring everybody together. Maybe it's because he thinks nobody would buy it if he did, or maybe it's because it's just not something he's interested in. But now he is saying it:
"I can change Washington, I will change Washington, I'll get the job done from the inside. Republicans and Democrats will come together." Now, this was off the cuff, and for all we know he may never repeat it. But in a weird way, Romney may actually be right. The chances of any significant bipartisanship are higher in a Romney presidency than in a second Obama term. Why? Because Democrats have shown over and over that they want government to do things. They'll compromise to get some part of what they want. They'll even allow a Republican president to get some credit. That doesn't mean they won't present a unified front of opposition at times (they did against Bush from about 2005 to the end of his term), but there's no way a President Romney would go through his entire term without getting any Democratic support for anything.
On the other hand, if Obama is re-elected, Republicans will almost certainly spend his second term repeating what they did in his first term. They'll do it because they think it makes political sense, and they'll do it because ideologically, they genuinely believe that everything he wants to do will lead America into a socialist nightmare. So bipartisanship can only come from Democrats compromising, which means it can only come if there's a Republican president.
But keep in mind that bipartisanship shouldn't be a value in and of itself. Any particular piece of legislation will either be good or bad on its merits, not because of who did or didn't vote for it. If Olympia Snowe had decided to vote for the Affordable Care Act, making it less partisan, would it help more people? No. The vote to authorize the Iraq War, the most disastrous policy decision in decades, was bipartisan. It's nice if people can cooperate, but what matters in the end is the substance.