Dawn - You're misreading what you quoted or I read too much into what you said. $3,700 is the amount of the deduction and has nothing whatsoever to do with the child's income if we're talking about a college student, which I was.
Lots of teens in their first job make more than $3,700 a year. The child's income has relevance to this discussion only in that, if he makes a higher salary, he can provide more than half his support and, thus, disqualify himself from being a dependent. This is not a number that the IRS sets. A child who goes to a $50,000 a year college requires more support than one who goes to a community college.