I'll caveat this by saying that when a new coach and GM come in, they will have their own judgements to make based on how they want to build the team. So regardless of his play, they may deem they want someone else.
Back to the here and now. This wasn't even a question a few weeks ago. It goes to show you how quickly things can change in this league. What has happened is he has hit the wall. It takes a good coach and supporting cast to help him through. If the QB can learn and adjust along with the coaches and other players, that's when a QB can grow and succeed. Will that happen with Sam? I don't know. Do they have the coaches and supporting cast to help him, I'm not sure about that either. But some adjustments need to be made. Other defenses know what plays are being run and what reads he is going to make. They know to pressure him and he won't make the reads and throws he needs to make. Basically, the defense is controlling his game right now instead of him dictating the game.
I agree with what others have said, this team has a bigger need than at QB. They have to build the offensive line. They have to get some more weapons on offense. They also need defense, but that's not for this discussion. So if the new management decides that they want to move on at QB, then what is the plan for the O-Line. It's the same debate we have had about taking a guy like Harrison. You get that WR, but you don't have a line to block to keep the QB upright to throw the ball. So with Sam on a very cheap rookie QB deal, to me the best plan is to stick with him and a vet QB like Brissett, while you build the O-Line and improve the TE position. If Sam really struggles out of the gate next year, then you have a guy like Brissett to come in and try to salvage the season. The expectation that next year this team is going to be a playoff contender is pretty farfetched. So next year is going to be a year to grow as a team. Why not roll with what you have, upgrade the other positions, and if the QB position is the issue, you figure that out the next year.
On that note, depending on how the draft goes, if they end up trading down a few spots (few being the key), I'd love to see them get a first rounder from a team that could be bad next year. And on the flip side, what a disaster it would be to see them trade this year and next years picks to move up only to have an awful season, giving another team a top pick. Think of what the Panthers just did this last year and how they have no top pick to improve on the disaster they have been.