If it makes him look like he's feeling the effects of pressure this soon into his presidency, if it makes it look like he might not be the stalwart type who can handle a long campaign or insurgency, then yes...it will get Americans killed.
Yes, he has a hard job. Yes, he's going to need breaks. But you never show it. You never ever under any circumstances let the public know you are having a tough time. As President, you are no longer just a private citizen. You're no longer just "some guy". Because "some regular guy" would wet their pants and cry in a corner if they had to consider nuking another country. Every action, spoken word, and move you make is watched by the world over. You must look like you're on top of everything. Your vacations are scheduled, you don't give the impression that you "need" them. You have to act like a damn immortal. The first few months are critical to the image your allies and enemies will perceive of the President.
If our allies percieve Obama to be a lightweight, how will the possible trade war develop? If they push for so long maybe he'll cave so lets not give in so easily this time (sorry Wess, the UK caves easy on trade deals). How far does Iran think they can push? You can be the Taleban is wondering just hard far Obama is willing to push an extended campaign in A-stan. Maybe if they hold on for a while longer the Americans will go away.
The President needs to learn to say, "this was a scheduled event" not "we wanted to get away from the White House". You always project as a stalwart individual, not a regular person unless its to pick up polling points with the public (see Gore's strategic campaign wife kiss). This is Public Relations 101.
The President screwed up. Rookie mistake. He just needs to learn the ropes.