Hypocrisy in politics generally means pushing specific rules/laws that counter the basic principles you believe in.
When you ask for smaller government, but demand a big military, that is hypocrisy. When you complain about government being too big - but push for regulations about abortion and gay marriage, that is hypocrisy. Conservative legal theories claim they are limiting governmental power, but when the conservatives like the governmental power, they are all for it.
But the same goes for the Democrats. When a politician that objects to racism calls NYC "Hymie-Town", that's hypocrisy. When the Democrats talk about the "right to unionize" - and then force people to pay for a union even if they don't want to, that's hypocrisy. Feminists legal theory demands equal rights - except when it comes to the right to give children up for adoption.
Part of what is going on is that people have secret reasons for believing certain things - and lie about it. You don't want to outright say you are against government being too involved in business, but are for it being involved in religion and sexuality. So you say you are against 'big government' in general. Similarly, you don't want to outright say you are in favor of unions because they vote for you, so you talk about 'rights'. In both cases, people modify the statements of their beliefs, focusing on things that are not their real reason but close enough to it. It makes for better speeches - but more hypocrisy.
Hypocrisy is founded on the inherent subconscious knowledge that our own personal beliefs are not ethical. We create ethical public reasons to convince others we are right. Then we argue based on those ethical public reasons.
This makes winning an argument hard. If you attack the stated principles, you can't win - because those are not the real principles. You can convince some independents that honestly believed the stated principles, but not the core believers. If you attack their real, hidden principles, they say you are insulting them, as opposed to arguing.
Now, this only applies to specific principles. On a more abstract level, things are different. Generic ideas are more straightforward. So often the key to converting the core believers is to strike for the very heart of their beliefs.
Originally, liberals were about progress. Originally conservatives were about conserving the good old ways. Now, things have changed a bit. As I posted earlier, liberalism is currently based on the core belief that people are inherently good, but bad things happen to good people. Liberals want to help the unfortunate get over the tough times, not protect them. Conservatism is based on the core belief that people are inherently sinful, but can overcome this with solid planning and hard work, turning good. Conservatives want to protect weak willed people from temptation, not help them.
But those ideas, because they were so abstract, are harder to argue. It takes a remarkable event to change them, or years of exposure to real life. You need a Job (bible Job, not Apple) like series of events to convince a conservative that even with good planning and hard work, bad things can happen to you. Similarly, it takes a horrible evil act to scare a liberal into thinking that all people are sinful, and that it takes work to become good.
But these events happen. September 11, 2001 was just such a tragedy and it scared some liberals into conservationism - at least for a little while. Similarly, Bush's economic disaster took the homes and jobs of enough conservatives to turn people liberal - at least for a little while. Some of those conversions became permanent.