Had the same problem, found a small piece of plastic in the line that hooks to the flex hose. There is a plastic piece in the end that has a check ball in it,that had the plastic piece in it. I removed the check piece completely with no ill effect.
Man, I wish I had read this post closer the first time. After 4 days of no water in the kitchen...no one to help..and plumbers don't make housecalls on RVs...I got really p****d, and ripped the whold d*...n*d thing out. The entire setup just did not operate right. And, my handyman was going to haul out and just buy another faucet. Enough is enough.
I read your message as a piece of plastic in the head of the faucet...what it woundup being was the check valve at the beginning of the flexipipe and it's a really, really small piece of hardware. My flex had TWO check valves. They're jammed in the end of the metal flexipipe, the part that is attached to the water inlet, and faucet head. You could blow a low melody on that thing...and then all of a sudden...it would snap closed and not even the air from an air compressor could blow it open. The plastic, instead of sliding, canted to one side and froze in place. No broken plastic piece, nothing just floating anywhere.
Through the judicious use of an icepick and a jackhammer, I got the little check valve removed and water now flows. Both checkvalves were removed and beaten to pulp by my ballpeen.
That was what it was. Take notes, guys...my plumber had never seen this particular setup before.