No. The amount you have withheld from your wages does not affect your eligibility for the Child Tax Credit. Although it will not affect the Child Tax Credit, you may still end up with a lower refund or possibly owing taxes, depending on how much they are withholding compared to how much you earn. If this is your second dependent, it would not change your filing status. Also, the fact that a Child Tax Credit is at most $2,000 means, they are not withholding that much more.
There are not dependent exemptions anymore, so even if you only get paid every other week, a $7,800 drop seems excessive for a change in your withholdings because you added a second dependent. If you didn't already have a dependent and you are single, then this change likely reflects the change from single to Head of Household.
You may want to contact your employer to find out why they changed so much.
Also, look at lines 16, 24 and 34. Then subtract $7,800 (if paid biweekly) to see where that leaves you for next year. Add in $2,000 for the Child Tax Credit (IF you definitely qualify) and if your wages stay relatively the same and you have no other income sources, this will give you a rough idea of your tax refund or amount due next year when considering your extra $300 per pay.
Also, if you are married, your spouses wages should be considered when you adjust your W-4.
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