No, it's not possible.
Even if you had no deduction or credits, your federal tax on $16,604 would be:
$9075 @ 10% = $907.50 +
$7529 @ 15% = $1129.35
That assumes you are filing as single.
There must be more to the story. Typo in your income numbers? Also, what do you mean by a self-employment tax deduction?
Maybe update your question to include a breakdown of everything you entered?
As noted in Loren's answer, it seems that it is indeed possible in at least one case (self-employment taxes).