A manager at my company cited a very vague New York law that I'm skeptical about. We can have no more or less than 48 hours to sign an employment contract. Is there any truth to this?
There is no New York law that requires you to accept a job offer at exactly 48 hours from the time that it was made, no more or no less.
A private contract can give someone 48 hours to accept. There are probably many workers in New York City who are governed by industry-wide union collective bargaining agreements (which apply to almost everyone in the entertainment industry) which regulate the giving and accepting of offers to some extent.
There may be a right to recission for certain kinds of contracts.
But there is no law that is an exact fit to the one you describe that would apply to an employee at a web based tech company.