The House will originate most of the bills in the next two years. So the complexion of any bills that get through the Senate will be conservative 99 times out of 100.
However if those bills get to Obama's desk they will require 'bipartisan' support. This means a few conservative Dems will always sign on dutifully. It also means Biden will be much more public in debates and votes there. (he'll be revived as a gaffe machine by the media no doubt)
So Obama has two options...
On the one hand he can sign off on essentially conservative laws sent to him from the senate and risk a primary from dissaffected liberals. If the wars go on and we have domestic austerity it will be tempting for someone on the left to primary or even run a third party challenge.
On the other hand he can veto 'bipartisan' bills and risk losing 'moderates'. Moderates like Nelson and Lieberman and Landreiu. Yuck. But that's how it will be portrayed.
So he's now got a complex political problem to solve that he would not have if the GOP had won 51 searts in the Senate.
He cannot run against an extreme Senate as any vote there would need bipartisan support to reach him. He's in pickle with this because he's always supportive of commity.
A third scenario is that the Dem Senate could filibuster like crazy ( but that of course is off the table after recent announcements) and would be cast as obstructionism. Liberals and progressives have nothing to look forward to but more war and domestic austerity.
at least in 1994 the Democratic President had a Senate and House to oppose. This time he'll have to threaten to veto bipartisanTM bills if he wishes to avoid a primary.
Sorry for being Marvin the Paranoid Android.