FileMaker interprets 6/27/2013 as 6 divided by 27 divided by 2013. The / is the division operator after all. If you have to use a literal date in a calculation, use one of these two options:
If (Date < GetAsDate ( "6/27/2013" ) ; 1 ; 2)
If (Date < Date ( 6 ; 27 ; 2013 ) ; 1 ; 2)
Phil is on target. His second choice is going to "always" be correct. He noted your use of the USA format of "/" serpartators, but many other countries have different order and separators. The Date functon will take D;M;Y and make the correct System format.
Good point. With GetAsDate, the quoted text has to be a correct date for the current systems locality settings.