I have this game, and find it actually quite fun.
It is important to read the manual, but other than that, if playing as a Democrat, stick to issues that appeal to Democrats And Independents, if a Republican, stick to issues that appeal to Republicans And Independents. You can tell which these are if you highlight the 'state details". Those with thumbs pointing up show that if you take a 'support' stance, you will get votes. Those issues with thumbs pointing down show that if you 'Oppose" this issue, you will get votes from folks who oppose them.
So the key is to avoid issues that split dems/independents/reps and try to support/oppose ones that appeal to everyone (like homeland security or public education, more jobs, war on terror) and avoid divisive ones like abortion, strong military, taxes. And whatever you do, Never change your stance in mid stream! If you're a Democrat, don't suddenly become anti-abortion.. it will kill you. Conversely if you are a Republican who is for high taxes, you can forget about getting elected. Support Always starts with your base.
If you are still having trouble, try to focus on the following states First and make sure they are in your camp (your color on the 'polling date' screen):
California, Texas, New York, Florida, Illinois, Pennsylvania, and Ohio in that order. If you can get these states on your side, your victory is almost guaranteed.
Try to build campaign headquarters in these states because this will increase your awareness (necessary to gain independent votes) more quickly. They will also increase your income. Give lots of speeches, dont get carried away with ads, but make sure you place a few here and there in the big states. And do all your fundraising in the rich states too (California, Texas, New York, Illinois, Florida). Lastly, dont forget to build up political capital. One endorsement such as the unions or the christian consortium (?) can swing over as many as 10 states to your cause all at once!
Hope those tips help, and Good Luck!
P.S. If you play in the campaign, every time you successfully defeat an opponent, you unlock a new candidate for the other party. I've been playing as a Democrat and have unlocked William Taft, US Grant, and Richard Nixon so far. There's 5 to go, I am guessing Teddy Roosevelt and the Gipper are in there somewhere too.

Now if you play as a Republican, you might be able to unlock some good Democrats... FDR? JFK? Who knows?
-Elgalad