Don't like offer

What is the name of your state? NY
I am employed at an hourly wage and receive no benefits, I am now being offered a salaried wage with benefits, but I don't think this package is good enough. If I turn this offer down. What will happen? Can they lay me off, and deny me unemployment benefits.

What WILL happen? Sorry, my crystal ball is out for cleaning.

What MIGHT happen? They MIGHT improve the offer. They MIGHT say, okay, fine, and fire you. Or, they MIGHT say, okay, fine and let you continue at your old position.

Assuming that they fire you, which is a possibility, THEY cannot deny your unemployment benefits. Only the state can. However, it is quite possible that the state might do so, since you turned down full time work. Most of the time, that disqualifies you for benefits.