I failed to notice that you said that you also made a personal contribution of $6,637. That means that your deduction on Form 8889 line 13 would be $7,900 (limited to the maximum permissible) and you would have a $674 excess contribution on Form 5329.
I'm questioning whether or not you actually made a $6,637 contribution in addition to the $1,937 that was made through your employer. Did you actually make only a $6,637 - $1,937 = $4,700 contribution separately from the $1,937 contribution made through your employer?
[Edit] Also, given that you reported total contributions to a single HSA of $8,574, resulting in an excess contribution of $674, that fully explains the $202 increase in federal taxes due when you add the $1,937 entry. That increase is 6% * $674 = $40 of excess contribution penalty calculated on Form 5329 and additional income tax of 24% * $674 = $162.
