Most public stations receive an amount that is less than sales tax as a percentage of their operating fund from CPB. I really doubt there would be many stations going under because of CPB funding going away. Public broadcasters have proven themselves to be resourceful and creative at generating funding and I suspect the very threat, whether it materializes or not, should be a warning to maximize talents at local stations to 'take it up a notch'. With that said, I'd worry about the survival of small stations where the local operating dollars are but a small fraction of the expenses, generally covered by the generous help of larger stations that might not be able to help as much as they presently do or offer discounted rates based on their ability to pay. In these cases, the generosity of radio people and the dedication of volunteers would likely prevent the demise of the smallest of stations.
Looking at annual reports, it is easy to see the CPB dollars are minimal lines on the 'income' sources. If stations are so much on the edge that they can't survive a small decrease it is a wonder any of them survive equipment failures or a lightning strike. Any station has a bit of a reserve to get them past any downturn. Add to that, at least Public Radio, is stronger than ever in listening audience and ability to generate Underwriting.
I looked at one Public Radio broadcaster. They manage to attract a nice audience (comparing signals received to actual listening, they have 150% compared to total listeners divided by stations received) and produce an income between donors and Underwriting of $2 per $1,000 in retail sales, a figure a commercial station would be happy with...quite happy (in fact donors represent 26 cents per $1,000 in retail sales with $1.74 per $1,000 coming from Underwriting). And that is not including any CPB dollars...in the neighborhood of 6% more.