<<It still might.
<<When Chamberlain took this stand , didn't it cost him later?>>
Your argument seems to be that if Chamberlain was accused of lacking patriotism for trying to avoid war with Hitler and the charge stuck later, the same thing could happen to Obama, that by not supporting the war the charges of lack of patriotism could stick later.
First of all, Chamberlain's patriotism was never put in question, as far as I know. He was charged with accepting the word of a liar in exchange for a very brief period of peace, and then having to face a much strengthened liar after he'd used the peace bought with his lies to strengthen himself. Patriotism was not the issue, being a sucker was.
Your analogy is kind of intriguing, because both situations depend on the lies of war-mongers and the credulity of those who are taken in by them, although in Chamberlain's case, the liar and the sucker are each heads of independent nations negotiating with one another; in Obama's case, the liar is the leader of the nation, the suckers are the elected representatives of the people of the nation, and Obama is the anti-Chamberlain, the guy who not only was not taken in by the war-monger's lies but actively stood out all too alone in the crowd as the one who refused to go along with them.