I could probably tolerate dating a liberal woman IF she respected my opinions, and was willing to either not discuss politics OR engage in civil discussion without vomiting out the leftist line on every subject. But she'd have to be pretty moderate for me to even consider a long-term relationship of any kind. Even then, I'd be wary. The last thing I would want would be to marry someone who undermined everything I believe in. There's something to be said for complementary partnerships, but not to that degree. You have to be reasonably on the same page philosophically. Complement each other in other ways (division of labor, or in parenting style), but you can't be happy with someone who is as foreign to you as someone in China.
Having said that, I can't figure Carville/Matalin. The sex must be fantastic (sorry for that awful mental image).
The assumption you make is that they have differing politics.