On its surface, this sounds like a rather appealing idea. However, once I started thinking about it a little deeper and discussing with some of my esteemed colleagues, I quickly became rather opposed to it.
This daily vote limit was one of the very first measures we put in place to keep people from just blindly upvoting every post they saw. Voting is like a currency; the only way to prevent rampant inflation and to keep it meaning something is to limit your supply of it. If we start allowing that daily vote limit to creep up, we'll wind up with nearly all posts in a private beta being highly upvoted. (The reality of the matter is that people upvote FAR more often than they downvote.) Even in a private beta, we want people to think about why they're voting; one of the reasons for having a minimum number of people committed to the proposal before it goes into private beta is to ensure that there is a critical mass that can generate feedback on posts even with limitations we put in place like the daily vote limit.
As it is, most private betas have so few posts that many people never run into the daily vote limit. I know in your original post you said that you typically run into this problem in the first two days; if that's the extent to which this is a problem, you could simply favorite the posts you didn't have votes for and vote on another day. Again, our private betas don't get that many questions; there's no reason you have to vote within minutes of a new post going up.