If an employer rescinds an offer after you make a politely-phrased counter-proposal, then that's a very combative attitude and I'd stay away from working there to begin with.
The only kind of employer who would react that way is one who routinely misleads and exploits their employees through sketchy tactics and ultimatums.
Corp (in 1 week): "Thank you, but we cannot entertain your offer. We wish you all the best in your future endeavors".
You: Ok, let's negotiate.
Corp: "We've just filled in the position with suitable candidate. We'll keep your resume in our database for 6 months in case we might get openings down the road."