As I understand it (and I'm certainly not a tax pro) the Tax Credit has nothing to do with deductions, which reduce the taxable income. The Tax Credit is applies to the actual tax paid, so any tax paid up to $7500 gets erased. Its money in the pocket for anyone who pays federal tax, regardless of their deductions. If withholding was paid there could be a large refund.
The only people who can't take advantage of this are those that pay little or no tax - which usually means low income, or retired and living off pension and savings, but little actual income, or a very clever accountant.
This is correct, but even in the latter instance, I believe that you have several years to carry that forward. Or you can I believe just get it added to your refund.