Rearranging for another deal

Whoa, but my main credit card issuer, the one I use for bills n’ such, is offering me a balance transfer deal! 4% for 6 months, not too shabby. I’m actually just trying to decide if I want to take advantage or not, although in the meantime I cancelled my one pre-authorized bill payment, in case I decide to take it. The only wrinkle is simply that this card doesn’t have a high limit, so I can’t actually move alot of my debt over, so the secondary question would be this: do I ask them to increase the limit so I can take advantage of the offer? Doing so would run me the risk of being denied because of my current debt load (remember: I can make all the payments on my cards, it’s just that my ratio of available credit to used credit is too high.)

Thoughts? Do I ask for a limit increase so I can take better advantage of the transfer deal? Or do I just use the current limit?