President Obama could do worse. Romney has a bad reputation among Congressional Democrats, so I can't imagine they'd cotton to this. In fact, it's highly unlikely. But what Romney, in a bipartisan fashion, was able to do in Massachusetts -- even with caveats -- is pretty much the same as what Obama wants to do on a national level. Karen Tumulty notes that Romney is the only American who can claim the provision of universal health care as a resume line. Didn't help him in the GOP too much, but that's another discussion. If Obama wanted to bring Romney into the cabinet, he'd have to balance him by appointing a pro-choicer to a top HHS post because there are so many controversial, sexuality-related programs in that department that apportion money. The thinking here is that Romney would be the White House health care czar and that a Democrat -- Gov. Kitzhaber of Oregon, maybe -- would move over to Health and Human Services.
What does Romney get out of it? Assuming that Obama's ship is merely listing now and that the economy has recovered perceptablly, 2012 is not going to be an attractive cycle year for a Republican to run for president. If managerial chops are what's needed, then Romney's resume cuts in... something that, again, the GOP didn't seem to much appreciate in 2008. Like Hillary Clinton, Romney might be willing to trade his political ambition for the chance to do something awesome for the country.
Highly, highly improbable that this will happen. On the other hand, Obama seems to be willing to look at the Republican bench when his own side falls down.