"Is there any kind of grace period that allows me to have worked for 3 days then quit and still be eligable to collect UC benifits?"
No. There is no grace period. If there is available suitable work you must take it. With the economy the way it is and the amount of people out of work they can't afford to pay benefits because you don't like your job. Lots of people don't like their jobs. Tough it out and find one you do like. You cannot collect UI benefits for quitting.