It probably doesn't affect your chances of getting funded, but any potential investors will have a serious discussion about how your employer views intellectual property. In our case (YouOS), once we had received funding, we had to rewrite what we had developed from scratch, since our old company's employment agreement was a bear.
My startup is about to go into fund raising mode, meanwhile I am still holding down my day job. Is this going to be a dealbreaker for investors?
It's not a dealbreaker for us. It becomes more of a dealbreaker as the amount of the investment grows. For VCs doing a multi-million dollar series A round, it almost certainly would be.
One of the main reasons I want to get funding is to be able to afford to quit my day job. I would have absolutely no issue with that being one of the conditions of getting investment. It would be a pleasure to fulfill.