I'm just not able to find any data to suggest that urgent care facilities are overwhelmed nationally. The data shows Covid cases down most places, testing down.
If you Google "Urgent care overwhelmed" there are stories...but not recent ones. They are from early fall when Covid was at much higher levels.
Anecdotally, I have gotten booster and flu shots recently at my pharmacy. No line then. Went to same pharmacy yesterday. No one getting a shot, no line. (Anecdote #1)
I got a PCR test a couple of months ago. Schedule was wide open. We walked in, got tests, saw no one but lab tech. (Anecdote #2)
Just went to their site to look for appointment. They are wide open. I can schedule anytime or just walk in. This is in a heavily populated urban area outside of DC. (Anecdote #3)
Covid testing rates per 100k folks are highest in Rhode Island, Massachusetts, Alaska, NY and Vermont and DC right now. New Jersey is middle of the pack nationally.
So by all evidence I can find, overwhelmed urgent care facilities due to covid testing does not appear to be widespread. But I am open to data (not anecdotes) to the contrary if anyone can find any.
This of course does not mean urgent care facilities are not crowded or even overwhelmed in some localities for a variety of reasons. Whenever I have been to one, I usually had to wait and this was my expectation.