The way most nuts fit on the faucet, if the gasket on the end of the pipe is not snug against the faucet fitting, the pipe will move about easily...meaning it's too loose. If the pipe is snug and doesn't "rattle" about, it's possible that you are tight enough.
A lot depends on the taper of the male fitting on the faucet and the gasket on the end of the connecting pipe.
Put a towel down in the bottom of the cabinet, turn on the water and observe for leaks. Have a helper at the water valve to shut things off, and a second helper at the kitchen sink to open the valve and relieve pressure if you have a leak. This way, water won't flood your cabinet and the towel will soak it up.
Echoing others, if you cross-threaded the nut, getting a plastic nut on a brass fitting properly will be a challenge up in that tight space. If you are lucky, you can do it, but laying on your back, reaching up behind the sink, is not ideal.
The correct way to start a nut. ALWAYS turn the nut "backwards" slowly and gently while applying slight pressure. When the nut is properly aligned, it will "settle" or "seat" itself on the threads. You will clearly feel it. Stop turning backwards and slowly start turning forwards (righty tighty), and the nut should go on smoothly. There are some times when I'll spin a nut backwards 3 or 4 revolutions without it seating properly, because I'm not holding the nut squarely on the bolt or pipe. Don't give up on backwards rotation until the nut seats properly. If you don't feel it, keep trying. It's as if a ball drops into a detent. It's that noticable.
A possible work around. You could get a proper brass "nipple" at the hardware store to add to the end of your existing pex pipe in place of the faucet, then add braided hose to the other end of the nipple and to the faucet fitting. Working in the open where you can see and you're not in pain partially laying in the cabinet, you'll have much better luck getting the plastic nut onto the nipple properly using the technique above. You'll probably be able to pull the pex forward and work comfortably sitting upright while doing this. From there, adding the stainless braided hose should be easy. Use the same nut starting technique when connecting to the faucet...backwards first until you feel it seat, then tighten. Your extra stainless braided hose will probably do a 360 degree loop at the top of the pex when connecting to the faucet, but that won't matter.
That's a lot less trouble than cutting and adding fittings to PEX. But if you'd rather do that, consider using
SharkBites to add the fittings. They are awesome. I've used lots of them over the years, and they have never let me down...on copper or PEX.
Good luck.