This is such a touchy subject and I agree with sideliner, 4 weeks would be a minimum in my mind. Everyone's contribution to this thread is great but I have to admit this is an area where there are no set rules to follow----none I'm aware of. With the summer so short and with Mother Nature always ready to screw up a welcomed weekend, missing a weekend because a TD waits till it is too late for anyone to enter another contest can be devastating to the kids' experience at the travel ball level. Most travel teams do not participate year-round. The summer weeks may be all they get.
The question about how many teams does it take to constitute a tourney is another point of interest. Each tournament director will have their own spread sheet as to how many teams are needed to break even for the event just as they have a schedule that tells them the maximum number of games they can play in a given weekend, a deciding factor for the maximum number of teams that can participate. Everyone will be different when considering the factors.
I've seen tourneys with only 3 teams in an age group play. There are normally multiple age groups so the number of overall teams playing can help offset the expense of diamond rental. Three doesn't sound like much of a tourney but depending on the quality of the participants it could be a barnburner compared to a 10-team Rec line up. The choice is yours and with the sport growing in popularity, we're seeing more and more tournaments being offered for Rec or League level teams to participate. While time will be needed to sort things out, it'll be up to the teams to do their homework and select a schedule that best suits your needs. I suggest you enter early, ask questions when entering about refund policies, pay in full, and get a confirmation you have a slot in the tournament. Anyone refusing to confirm entry when money has been sent is definitely throwing a red flag in the air. You should have a confirmation within 2 weeks of mailing your money.