Line 35 on your 1040a is the amount of "Child Tax Credit". This is different from the "Additional Child Tax Credit" which is what Parts II, III, and IV on the 8812 is trying to determine. It is also different from the total child tax credit that you may be eligible for.
Did you do the "Child Tax Credit Worksheet" referred to in line 1 of the 8812? This is in the 1040A instructions for Line 35.
Line 6 on the worksheet will give you the total amount of child tax credit that you are eligible for. Note that if this amount is greater than the amount of tax due you have on line 30 (after accounting for the credits on lines 31 to 34), then you can take only enough of the tax credit to reduce your tax due to zero.
Line 10 on the worksheet carries to line 35 of the 1040A. This will answer your main question.
For example, suppose you have 3 children but your line 30 is $2000 (assume that lines 31-34 are zero). Then the Child Tax Credit is only $2,000, because you can't take more Child Tax Credit than there is tax to credit it against.
However, the other $1,000 is not lost. In most cases, you can take it as Additonal Child Tax Credit on line 43. In this case, you have to complete the 8812, and transfer the amount on Line 13 of the 8812 to Line 43 of the 1040A.
TurboTax, however, does this all automatically. Did you override some numbers on forms in TurboTax?