I'm going to try to attach a link, which leads to some pretty articulate discussion, both pro and con, for the Stolen Valor act. You can read in a few moments what would take me hours to compose.
http://www.scotusblog.com/community/...len-valor-act/
One older supreme court case scholars discuss holds that "false speech receives no protection". (I believe the case name is
Gertz). I have not studied this case enough to be able to comment upon whether it would apply, in whole or in part, in the present context. However, if the Court followed this rationale, the result is that the SVA is constitutional, as this defendant clearly lied about his military service.
If the Court were to strike this law down, they will have to be careful to avoid opening a Pandora's box, in that both the Feds and the states have lots of laws the criminalize lies in various contexts.
I notice that some lawmakers have proposed amendments that would add a "damage" requirement to the law, which would mandate a finding that a defendant gained something, money etc., in order to impose criminal sanctions upon a defendant. Whether those hit the floor of Congress will depend on the Court's decision in this case.