The "Google union" is a complete joke BTW. It's made up of half a dozen low-level employees that have no bargaining power at all. Half the company hasn't even heard of it (true story).
That's unnecessary. I'm simply demonstrating that unionization has occurred in businesses far larger and with arguably more difficult organizing environments than Basecamp (with a total of ~60 employees). 800 Google workers thought it important enough to join their union.
A Basecamp union organizer who was the only one to decide to join their own creation of a Basecamp Workers Union would already be 3 times as successful as the Google union on a per-capita basis.
A union derives its bargaining power from the amount of monopoly it has on the labor supply. (I don't say that as a bad thing; I mean it just as a factual thing.)
Tech industry turnover is around 13% per year, or 0.25% per week. The Google union could all quit at once and it would be like that week's turnover number was slightly higher than normal.
Google has more employees out sick on any given day than they have union members.