Is...is this something that's good for your career? Is it a promotion? Is it a lateral move?
If it's a promotion you didn't ask for, and you turn it down for very clear reasons, AND you're doing a good job at your current role, there's a good chance you'll be fine. After all a valuable employee at Position X who turns down a promotion to X+1, is still valuable at X. However, it is likely that future promotions will be unavailable to you, at least for a while, as you'll be perceived as "happy where you are"
On the other hand, if you're being moved laterally to a non-technical position, there's a decent chance they say something like, "Well, lunchlady55 is smart, and very organized, good manager, but not really hands-on technical enough for what we need. We don't want to lose lunchlady55, but we're suffering because of L55's technical weaknesses. Why don't we move L55 laterally to a project manager-type role where we can leverage his/her strengths and backfill the technical position with someone who's very technical but requires lots of oversight"
In that situation, they're actually being good managers, by recognizing that they have a valuable employee who is just in the wrong position, and trying to rectify the situation. On the gripping hand, they're being bad managers, because if this is the case, it should really be explained to you.
If the latter situation is the case, you put them in a much rougher position, because they like you, but you're not meeting their needs in one area or another. In this case, you may lose your job.
The best way to handle this is to have an open and frank conversation with your manager. Talk about what the organizational chart looks like. Who will you be reporting to? Is there a raise or other compensation for being on-call? Be frank - are there concerns about your current job performance that led to this lateral move? Are they eliminating your position and they're just trying to protect you personally?
Based on all this, you can make an informed decision about what the situation is. You may want to try to negotiate yourself a better deal. For example, you're on call for the weekends, but whenever you have to do off-hours work while on-call, you get 2x that amount of time off your regular day during the week. Or you get paid for on-call time. Don't try to negotiate this until you understand why this is happening.