No. You cannot contribute to a 2016 401(k) after Dec, 31, 2016 - only IRA's for 2016 can be contributed to before April 18, 2017 and only Traditional IRA's are deductible if not limited by the amount of your MAGI.
And 401(k) Roth contributions will not lower your tax since they are after-tax money.
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**
