First, how is your company doing business now without a PE? Did the last guy quit? Are there others trying to get their PE? Why were they discussing it and why were you picked? Were they having a management meeting and realized they didnt have someone and they said "Oh Joe over there has his PE, lets make him the guy!" What's your relationship like with the company?
The reason I bring this up is because there's a lot of red flags here. If they say that your responsibility wont change, then they're just using you for your stamp. Your responsibility wont change, but your liability sure will and you need the responsibility (and pay, authority, and title) to go along with it.
So what are the company's options? It's you with a pay raise, or hire someone else that will cost them a lot more because they'll likely have to advertise the job as principal engineer or engineer in charge or something and state on the job description that the job is for the "it" guy.
If I was in your position I'd tell him if you're the "it" man keeping their business in the engineering business, you want to be a partner. It may require some investment on your part, but if you like the company and want to have any kind of respect from your higher ups other than the fear that you could leave at any time and will make them out of compliance with state law, then you need the responsibility that comes with it. If there's significant liability involved, which there is since you're the only guy with the PE, then your name should be on the door.