Jack Ryan: General, the President is basing his decisions on some really bad information right now. And if you shut me out, your family, and my family, and twenty-five million other families will be dead in thirty minutes.
President Fowler: Order the planes to stand down, take us to DEFCON-3... and will somebody ask Mr. Ryan if I can use the phone now?
President Fowler: We gotta update these fire drills, Billy. I mean, if the shit ever hits the fan, I'm not going underground. This place is a goddamn tomb down there.
Bill Cabot: We've also gotta choose someone else to face off against besides the Russians all the time.
President Fowler: Really? Let's see. Who else has 27,000 nukes for us to worry about?
Bill Cabot: It's the guy with one I'm worried about.
President Fowler: We have finally learned, at far too great a cost, that if the most powerful weapons ever created are ever unleashed, they will be fired not in anger... but fear.
Jack Ryan: I don't go on the, you know, missions, I just write reports for the CIA.
John Clark: Then write a report about it.
President Nemerov: For you to get involved here, its like sleeping with another mans wife... and what you are suggesting is that afterwards they all live together under the same roof... but what really happens is that the betrayed husband goes out and buys a gun.
Answer: The President telling Cabot to "get the people out of here" is just a political life boat. If asked what he did when he found out about the bomb he can "honestly" say he asked for an evacuation.
It's unlikely at such a time of panic that one would consider a 'political life boat'. There's also nothing in the character as presented to suggest that would be his thought process. The president's just been told that there's a bomb in Baltimore (not the building) and says "get those people out of the stadium." He's being evacuated from a location that contains thousands of other people. It's fair to assume he knows all those people are also in danger so wants them evacuated too.