There is a line of thought that holds that Republican control of Congress could help Obama in 2012, by giving Republicans some responsibility for the state of the economy. Research (via John Sides) suggests it doesn't work that way:
Consider the 1992 and 1996 elections. They featured opposite configurations of divided government, with a Republican president and Democratic Congress in 1992 and the reverse in 1996. Political scientist Helmut Norpoth investigated voting behavior in both elections and considered four possible "verdicts" that voters could render. One was a hung jury, in which voters could not agree on who was accountable for the country's situation. A "split verdict" meant that voters reward or punish both parties equally. Or, voters could simply give all praise or blame either to Congress or to the President.
Norpoth found that voters hold the President accountable:
Under both Republican and Democratic Presidents, and with Congress in the hands of the opposite party each time, voters assign responsibility for the economy to the President, not Congress; at least, they vote as if they followed that logic.
In fact, another analysis of over 40 years of presidential elections, this one by political scientists Richard Nadeau and Michael Lewis-Beck, found the same thing. Voters rewarded the president's party when times were good and punished it when times were bad -- no matter whether government was unified or divided. Nadeau and Lewis-Beck write:
The presidential office is viewed as the command post of the economy, irrespective of whether the president actually has sufficient control of Congress to implement his or her economic plan.
That's where the 2010 election seems likely to leave Obama. Under divided government, he'll have less power but no less accountability. Of course, if the economy turns around, a Speaker Boehner won't matter one way or the other. But if the economy continues to stagnate, blaming a Republican-controlled House or even Congress won't help Obama.
I do think there is another, more subtle political benefit to a GOP Congress: It would allow Obama to position himself in opposition to some unpopular people and their ideas. But that's going to happen in 2012 anyway when the Republicans nominate somebody.