I thought we would have plenty once they put the budget to extract it.
My understanding is that you're correct. There's a "shortage" of lithium because it's not being mined, not because there isn't enough to mine. You'll also hear that China has all the deposits, but again, they're the only ones currently mining it in large volumes, not the only ones that have any deposits to mine. One of the largest deposits of rare earth metals is in Nevada, IIRC. I think people hear the term "rare earth metals" and don't realize that "rare" is relative. There's a lot less lithium around than, say, aluminum, but we don't need all that much in the scheme of things.
Would Elon Musk be involved in doubling the world's manufacturing capacity of lithium batteries if there was a huge bottleneck like that in the way?