Realistically, if the PO can’t convince the CEO that the PO is right, the PO can and possibly should be removed or the project canceled. Budgeting or other issues (possibly outside of the PO’s scope) may make a project unfeasible or force the POCEO to reevaluate the scale and priorities of the project, but within those limits, if the PO can’t make a case for the project, one of the two (possibly both) should go.
That’s assuming it is a significant disagreement, if the issue is trivial then resolution is likewise trivial.
How this affects the team can vary from not at all, to all of them finding pink slips on their desk the next morning.
What the PO should do in this situation, will depend upon just how messed up things have gotten, the relationship between the PO and the CEO, and other factors that will very much depend upon the situation. The best thing the PO could do, would be to avoid it entirely, and not allow the situation to degenerate so far that the CEO has lost faith in them.