The banks absolutely have that power, and it really wouldn't take any effort to make it happen. All financial institutions rely on one another to protect their own investments. Most people bank with big institutions, including the exact ones we're talking about. A lot of people have BofA bank cards, or use Chase Bank (which is JP Morgan Chase). All those banks have to do to shut down your withdraw amount, is to just do it. And they would absolutely do it to keep you from preforming a run on the bank. Not only that, but the government would get involved in stopping you from engaging in a run on the bank. Including shooting you, but I don't think we'll see too many shootings or arrests, because it won't make a difference.

Literally all of those things are quite easy to do for the banks, or are otherwise easy to coerce smaller banks and credit unions to enforce.