Call me crazy.
I think the limit is some high fraction (greater than 50%) of the number of high schools in the country. 10,000+ teams.
It’ll take a couple decades. Growth is occurring, but it is governed by a small group of enthusiasts and hard workers exciting individual schools around the country. So its gonna take some time. I’m not counting on exponential growth.
I know, 10k+ is a lot of schools. You’re thinking, who the heck is going to pay for all of these teams? But here’s my scenario.
The number of teams continues to grow slowly in the areas where FIRST has a solid foothold. Employers who need engineers are here, and they will continue to see that FIRST is raising the quality of engineers, scientists, and technicians. In order to compete globally, they need these people. Designing and developing new stuff - stuff that works, that people have to have - is what its all about. The employers are in it forever.
Many teams will be funded for the most part by these employers. I think there are many more employers left to sponsor teams, in all parts of the country. They just need to know more about FIRST and the impact it has.
In 10 years, having FIRST experience - in high school, and in senior year of college - will be expected of top engineering grads. Teamwork, first-time-quality, meeting deadlines, competitiveness, … “What did your team do, Ms. Prospective-new-hire?” “You’ve been on our team for 8 years now Billy, and now that you have your degree, we’d like to hire you. You already know all of your co-workers and how to get stuff built in our shop. Heres your pocket protector and ID badge. Get to work.” 
But thats not all… School districts are realizing that “project-based learning” and “engineering 101” experiences are good for their kids. Principals are going to make sure they have a decent electronics lab, computer lab, and OMG they need to get a shop class back in the building because they need to build stuff for those electronics and computers to control. Drill press, bandsaw, lathe, mill, NC controls - YES, they’re gonna need em. The labs and shops will satisfy the vo-tech crowd AND the college-bound crowd. This project-based stuff (“reality education”) is imho trickle-down from what has been going on in engineering universities for over a decade now.
Parents (the ones who vote and pay taxes, the ones that make school boards jump) are going to realize that their districts need to keep up with the Joneses. They will vote for this stuff because, hey, last week on TV they saw a thing about some robotics comp and the kids were psyched about … LEARNING! They’re gonna vote for that stuff bigtime. Someday. After they hear about it or see it.
So additional funding will come from parents who learn about FIRST, learn that it takes some basic elements at the school to do FIRST right - math and science teachers, computers, electronics, a shop - and they’ll vote for it. Right alongside the new football field with that cool fake turf. One district after another…
Other parents/schools, in areas where there are fewer hi-tech employers, will want to do the same things because they will see what the FIRST-aware high schools are doing. They will want to have this stuff in their schools too. So, as soon as they hear about it…
[this paragraph might belong in the rumor mill] Companies who want to get people’s attention (yeah, all companies) are going to need other ways to advertise. Think about how much is spent on TV commercials. Well, once everyone has tivo and commercials are not so effective, once the shows themselves are saturated with product placement (love those Hummers on CSI, don’t ya?), companies are going to need to spend some cash on other forms of product placement. This is where our cool robots (and cool robot games) come along. “Excuse me, Mr. Gatorade-seller, you want to give me $4000 in exchange for a 4” x 6" decal on my bot? It’ll probably be on TV at the Detroit Super-Regional in March, and maybe at the Championships in April, and if we qualify it’ll be in the International Robotics Grand Prix in Kokomo in June. I’ll put it right under my (insert main sponsor here) logo. Can you give us a couple of cases of Fierce Grape? It’s hot in the Superdome in April…"
I think people (companies, principals, districts, parents, advertisers) will pay because they want to. Its the American way isn’t it?
Assuming, of course, we are exciting enough to get, and stay, on TV.
Ken