I don't think I'd pursue that approach. The figure they named signalled their expectations. I think it's best to just say you're too far apart and that you're going to move on, and do so. If they want to come back with another offer, they can, but their initial number was a non-starter.
Have to agree with this. It’s not just this year’s comp to worry about. If they think your best alternative competes against $45K, what’s the prospect for your future raises? And stock grants?