A single power. And I don't think it's a power all mods have. If it is, it would only take one rogue mod to re-public the subreddit.
And really, whether or not the mods continue to moderate is the thing being tested with such a move. Reddit did the API thing, the mods responded by escalating to this. Reddit can either blink and walk back some of their choices, wait for the mods to blink and reopen (of which, some have already), or reddit can escalate further and see if that makes the mods blink.
I believe a non-zero number of mods will continue to moderate. I also believe there are more than enough people willing to moderate to replace any of those who refuse to return.
Then you have weird situations. Because I'm willing to believe that some people believe it is extraordinarily difficult to moderate a subreddit and that they are uniquely gifted at it. Some of these people will believe that they have to moderate the subreddit because they believe the community will go to shit without them. Others will believe that their replacements will cause the community go to shit and Tim Reddit himself will come begging them to rejoin the moderation team.
And neither of these things are true. Moderating a forum is mostly drudgery and the only real skill it takes is having the time to do so. This is a battle I don't think the current mods can ultimately win.