When I interview, I mention that I have to give my present employer 2 weeks notice, whether it's true or not. Then I carefully watch their reaction. Anything other than supportive is a deal-breaker. Either they have integrity or they don't.
On the flip side, when I am interviewing a candidate I always ask when they would be able to start if we were to make them an offer. A currently employed candidate who says "tomorrow" raises huge red flags.
Screw that noise. It is clear from just that they don't respect people's time.