Since there is no way Rand Paul is going to win in 2012, we will have to assume that Obama will be reelected.
Obama's approvals are about 35-40%. The economy begins to make a comeback from the late-2000's recession; however, the national debt is inching close to 20 trillion and SS, Medicaid, and Medicare are all going bankrupt. The War in Iraq has been over for about 4 years, and an end to the occupation of Afghanistan is in sight. However, both Iran and North Korea now have fully operational ICBM's and about 30% of Americans support going to war with either Iran or NK. Rand Paul runs as a pseudo-libertarian candidate, pushing for less government welfare and an isolationist foreign policy. Caroline Kennedy (who was elected to the Senate when she defeated Scott Brown in 2012) runs as a Obama-copy pushing for more government welfare programs and public option health insurance reform.
Using 2008 EV's:
Rand Paul/Bobby Jindal--302
Caroline Kennedy/Alexi Giannoulias--236