I'd say reaching 20 USD before the end of summer is much more likely than not. This is because I think the correct valuation of a bitcoin at the moment is higher than 20 USD. Consider: if Bitcoin becomes even a niche success---say, the standard currency for online gambling in a few regions---it will have to be valued at well over 1000 USD to accomodate all the demand. I'd say there's at least a 2% chance of that happening, which gives a value of 20 USD even if the only other possible outcome were total loss.
Over summer, many bitcoin users who are in school---like myself---will have more time to pursue Bitcoin-related projects. I have a business idea or two myself that I'd love to implement, and plenty of friends who still haven't heard my "sales pitch" and whom I'll see this summer. We're also seeing more and better press hits lately. It's probably a matter of months before Gavin is being interviewed on network TV. Meanwhile, look how fast we moved from $1 to $2---do you really think the jump from $10 to $20 will be much harder? I would only be mildly surprised to see us touch $20 this month.