This is something I advocate every year, but apparently not too many people are listening. For example, in AL LABR, I had a hole in my outfield after Jerry Owens got sent down and in my pitching staff after Matt Clement retired (which I appreciate because I'll get the $1 I wasted on him back). So I bid $16 on Santiago Casilla, figuring he could be a useful reliever with a chance for some saves, and $18 on Josh Anderson who could see semi-regular at-bats and steal 20 bases.
That was 34 percent of my budget gone after the first week, and I bid that much because I thought I would have to. It turns out the second highest Anderson bid was 9, and the second highest Casilla bid was 6. So ideally I would have spent 17 instead of 34, but I had no way of knowing that, and I wanted to be sure to get both. (DeWayne Wise went for 22, incidentally, and I bid 18 on him also).
Part of the reason I'm so aggressive with FAAB early on is because you get more for your money. Players rostered in April or May give you 4-6 months of production. Even if you save your money for a star at the July 31 trade deadline, you'll only get him for two months.
Moreover, if other owners are paying attention - and in LABR most are - they'll realize that as long as I have money to spend, I'm going to throw it around on decent players. So they have two choices - back off, and let me get the player, or spend much more than they'd like to ensure that they get them. Because the next time someone decent is available, I'd have no problem spending $40 if I thought the upside justified it, and that it might take that much to get him.
Two years ago, this worked out well for me when I got Carlos Pena and Al Reyes early - both were huge in an AL-only league. Of course, I've also spent plenty on scrubs who didn't pan out, but that's okay. Some of the teams that waited for the trade deadline still got beat out by other teams with full budgets anyway.