Can you make 403b contributions after December 31st count towards previous year tax return?

No. The 2017 403(b) contributions must be made by Dec 31, 2017.

No, 403(b) contributions function similarly like a 401(k) and are made during the tax year. IRA and Roth contributions can be made for the prior year up to the due date of the tax return.

So there is no way to decrease tax liability after Dec 31st if I am not eligible for IRA contribution deductions? : (

The only other consideration would be an HSA funded for the prior year up to due date of return.