So it's definitely worth a shot. But I wouldn't overdo it. You'll could easily across as being too demanding then.
The reason I've come to this conclusion is because there is one blogger in my network who now includes the request in pretty much every single tweet he sends out. It's just so tiresome. And it makes me feel resentful and annoyed. Frankly, I'm even thinking of unfollowing this guy. And that's saying something because he is a good blogger. I'm sure I'm not the only one who's thinking this way ...
The reason I find it so annoying is not just that it's so predictable. It seems to fly in the face of the whole spirit of Twitter. The microblogging site is all about freely helping and informing others.
Sure, everyone is on there to promote themselves, a businesses or a cause. But the best way to do that is to be as generous as you can. Give without expectation of reward, and it will all come back in spades. So if someone is always asking for something from his followers, it really stands out.
That's not to say you shouldn't ever ask for retweets. Like everything, moderation is key. Just include this request from time to time. Then it will not seem onerous, and people will be happy to oblige more often than not.