Damn it, every time I see a thread with this title, or something like it, I think of this wonderful little clip (from this).
Being extraverted doesn't necessarily mean much when it comes to dating; those with quirks can more easily put people off if they come on too strong, for example. More importantly, there's a big difference between natural introversion and insecure avoidance, and that needs to be considered. I personally love introversion, but I can't stand avoidant, insecure behaviour with anyone I'm intimate with, friends, family or mates.
Being yourself is what needs to happen if you want to attract someone for a long term relationship, otherwise, when things really get going, it's not as likely to continue for very long. If being yourself doesn't work, then it may be best to really take a closer look at yourself, your habits and behaviours (which may well be negative or unhealthy), and patterns in your attractions/who's being attracted to you. No one wants to walk into a relationship where they'll be saddled and strangled with someone's negative emotional baggage, which is a good idea--negativity can bring another person down no matter how much they love you.