It’s very commonly asserted that this is the case, but I’ve never really seen it backed up, and it would raise grave constitutional and political questions if it were the case.
The Secret Service can certainly advise, recommend, cajole, or plead with the POTUS. The agents assigned to the President’s actual protective detail could go so far as to threaten to resign en masse if the POTUS persists in some foolish and frivolous course of action. (“But I like driving around with the top down in my bright red convertible with the personalized ‘POTUS’ license plate. And if I don’t announce where I’ll be on the official White House web page at least 48 hours in advance, how will the crowds of my adoring fans know where to show up and throw bouquets of flowers at me?”)
Of course in the face of some immediate threat–“GUN!” “BOMB!” “KILLER RABBIT!”–the Secret Service agents can (and I’m sure would) just sort of physically dog-pile the POTUS and drag him off to safety. But to give the Secret Service the actual legal authority to override the President’s decisions would raise very serious issues about who is actually in charge of the country. As has already been alluded to by Chronos, even something as unlikely as an impromptu visit to the capital of a semi-hostile foreign power could be a wise and statesmanlike decision, necessary to avert World War III or coordinate Earth’s defenses against the impending extraterrestrial invasion or something like that.
We really don’t want an unelected and unaccountable “Praetorian guard” with the authority and power to override the decisions of the person designated by the Constitution and (indirectly) chosen by the American people to be chief of the executive branch of the federal government and commander-in-chief of the armed forces. (Note that none of this has anything to do with whether or not you or I personally voted for or approve of the current occupant of the office.)