A "fully refundable" credit, like EITC, is one you receive even if it exceeds your "tax liability" -- i.e., actual taxes as computed on your return (tax tables plus Schedule 2) less certain other credits that aren't refundable (like this one).
Tax liability is NOT affected by how much was withheld during the year; if a non-refundable credit reduces your tax liability to zero, you still get a full refund of your withholdings (plus refundable credits). Reducing your tax withholdings will NOT reduce your tax liability; it only reduces the amount of your eventual refund, not the actual credit. Thus, reducing your withholding will let you essentially get the credit faster. (Edit: As financial advisers will tell you, a refund is a psychological positive; but over-withholding is essentially an interest-free loan to Uncle Sam. Thus, it's usually better to reduce your withholding to get a smaller refund or even owe a small amount on April 15.)
The reason I suggested you NOT claim this via withholding is there are certain exceptions to the current credit that might cause issues. In addition to the non-refundable limitation, the credit can be phased out for specific manufacturers once they sell 200,000 eligible vehicles; GM & Tesla are already ineligible for this reason. If you reduce your withholding assuming you'll get $7,500 but don't get that much, you may owe bigtime next year -- big enough that you may owe an underestimate penalty.
Finally: Your quote from President Biden probably refers to enhancements proposed in his Build Back Better bill, which has NOT passed Congress and is being reworked; such a proposal may OR may not pass. I am referring to what is law now; I cannot predict what Congress will do by this time next year, so I have to assume present law.
