First of all, Puerto Rico doesn't really have Democrats or Republicans. It has the New Progressive Party (Pro-Statehood) and Popular Democratic Party (Pro-Commonwealth). The NPP on the whole is center-right and its members affiliate with both the mainland Democratic and Republican Party, whereas PDP members almost entirely associate with the Democrats.
So, for example, Luis Fortuno was a libertarianish guy who was a Mitch Daniels-style spending hawk who was liberal on some social issues like gay marriage and marijuana policy - so he affiliates with the GOP and was talked about as a potential running mate in 2012 for Romney. On the other hand, the current Governor Ricardo Rosello is a centrist with a background in finance and affiliates with the Democrats on the mainland. Both are NPP members. Odds are, Puerto Rico will continue to have its own two parties due to the linguistic split from the mainland.
Plus, Puerto Ricans on the island are very purple voters. Mainland Puerto Ricans who were born in and grew up in the mainland tend to vote Democratic, but new arrivals to the mainland have tended to be swing voters.
Puerto Rico will probably have a better financial situation since they won't be able to borrow as much money at lower interest rates than they should due to being a US state rather than a commonwealth. They'll have to pay more federal taxes however, so I don't see why Puerto Ricans wouldn't end up as anti-tax advocates since new taxes will be a pretty sudden shift. Puerto Rico will likely join Hawaii in being opposed to the Jones Act. I can see PR trying to do what Florida did OTL and become a center for companies fleeing the high taxes of the northeast by having a low corporate rate and comparably low income taxes (today it's 4% in PR, for example).
As for Presidential elections, PR probably makes Florida a moot point in 2000 if they go for Gore. However, I think Bush is likely to win Puerto Rico given his strong hispanic appeal and his ability to campaign in Spanish.