I seem to recall reading somewhere that most kickstarter projects get the bulk of their support at the very beginning and end, with a "trough" in the middle. It seems like a good prediction model would take this into account, perhaps by integrating data from a number of similar projects that have finished funding (big-$$ games, other hardware projects, etc.)
My suspicion is that the wave of support at the end is for projects that haven't yet reached the funding threshold (thus, backers have an incentive to push friends/family/twitter followers to also fund the project).
I'd be somewhat surprised if said final wave occurred for projects like this, which blow past the threshold well before the deadline.
As well that many people end up wanting to see if this is really going to get the support and actually happen, because only then is it really worth pledging their money.
I think another part of why people support (product-driven) projects last minute is that people are debating whether they want one. There is no consequence to wait for the last minute and I bet many people, myself included, are debating whether it is worth buying one.
You would need historical data then, which I doubt kick starter would provide. Only way is to check the amount and # of backers every minute, on every page, unless I'm missing something. This would be incredibly useful information for people looking to use kickstarter, but I don't think kickstarter would be too happy about that being readily available. IMHO, all the more reason to get it.
I wrote a perl script to pull data from kickstarter. The backers page on the kickstarter page lists all of the backers, and the date that they made their pledge. I wrote a script to pull these dates.
Data are only available at day level granularity, but it's pretty good. Check it out on the bottom of the post.