Would Obama Win Re-Election While Losing The Senate?

[Skill and Chance]

A gain of +4 seats by the out party hasn't happened since the 17th Amendment in an incumbent president reelection year.  Historically it has either been fought to a draw or there have been massive gains for the president's party.  That doesn't mean it's impossible, but there are certainly a large number of senate democrats whose seats would be saved if Obama wins their states.

The way I see it, getting that 4th net seat to flip will be the big obstacle.  They probably beat Ben Nelson and Claire McCaskill and someone else in a reddish state retires, but with an Obama win the Dems probably pick up MA or NV.   

[Skill and Chance]

My guess is that if Obama wins re-election, he'll do so with fewer electoral votes than in 2008. The only other time this has happened is 1916, where the Democrats lost 2 seats.

I will hazard a guess that there is a strong correlation between Obama's vote share and how many senate Dems are left, more so than a win vs. a loss.  Ex:

Blowout Obama loss (<40% of the PV): ~GOP+11 (basically everything outside of the Northeast/West Coast falls)
Narrow loss (GOP <300 EV): ~GOP+5
Statistical Tie or EV/PV split: GOP +2-4
Wilson-style narrow win (<300 EV, PV closer than 2008): ~GOP+3 to Dems +1
Blowout Obama win (>58% of the PV): ~Dems +6 or better (this is where they start winning in AZ, TX,TN, etc. because Obama carries those states)

Also, remember that Nelson and Lieberman will likely go down, so 50-50 would likely mean true D control under Obama's VP.

[Skill and Chance]

In 2004, Bush's party won four seats.
In 1996, Clinton's party lost two.
In 1984, Reagan's party lost two.
In 1964, Johnson's party gained two. 
In 1956, neither party gained.
In 1948, Truman's party gained nine.
In 1944, FDR's party lost one.
In 1936, FDR's party gained five.

This amounts to an average gain of one seat.

These results tell me that there isn't really any apparent trend to be found here, or any hint of what we can expect should Obama win in 2012.

To answer the question: Yes, there is a very real possibility that Obama could win re-election while the GOP takes control of the Senate.

The "other" party gaining 4 seats during a presidential re-election would be a new phenomenon since the 17th Amendment, but the House flipping without the Senate was also a new phenomenon in 2010.  So who knows?