Politicians lie for a very simple reason: to get more votes. It's a reality of politics that not every person in the country will agree with your goals and beliefs. Maybe not even a majority of the country (or state, city, or school-wherever the election is taking place) will agree with a politician's positions. Having to please enough people to build a majority of supporters means that, as a politician, you have to tell people something that will please them enough to get them to vote for you. Crooked politicians will tell one group of people something in Florida, and then tell a different group the complete opposite when in Ohio. Fortunately, our founding fathers established freedom of the press and speech in our constitution and we can point out these discrepancies, especially in the age of YouTube. Even so, the ability to point out candidates' lies and "misspeaks" is irrelevant if the people who are voting don't pay attention enough to realize that they are being lied to. When a large chunk of the population doesn't make up their mind about who they are going to vote for until they get into the voting booth, that tells me that likewise a large chunk of the population is apathetic and uninformed. They hear something told to them by a candidate in Florida and go vote without realizing that the candidate said the complete opposite in Ohio. Which leads me to my second reason why politicians lie: because they can. Only very politically inclined people and those who really scrutinize the news are the ones that can actually make the connection of when a candidate is or is not lying. Only the well informed will know when lies are being told, and I think that a small percentage of the population pays this amount of attention. The rest of the population can be lied to and it will not affect how they vote, since they don't realize the politician is lying to them and thus their vote is not swayed.
Since a lot of the population falls for that kind of trickery, it is to the politician's benefit to lie to different groups of voters. You go around the country telling people what they want to hear--even if it's not the truth--and you will gain a lot of support in the uninformed voter demographic. That's why Thomas Jefferson stressed the importance of a "strongly informed and well-educated electorate", so that a majority of voters know their stuff and can make informed, educated, and well thought out votes when they go vote, and not just close their eyes and fill in ovals.