I don't understand your employer's argument, certainly there are no rules that more federal taxes should be withheld in January than December. The formula doesn't change from week to week.
You do need to be sure you are looking at federal withholding only, and not mixing it up with FICA (social security, 6.2%) and medicare (1.45%); those should be listed separately on your pay stub. And it is true that FICA stops after a gross income of $127,000 and resets in January. So if you make more than $127,000 per year, your total withholding will go up in January, but it's FICA, not federal withholding.
The tax table is here, you can calculate exactly what the withholding should be for your allowances and income.
https://www.irs.gov/pub/irs-pdf/p15.pdf
Note that the IRS will be releasing new tables in February to account for the new tax law changes, so you will want to review the new W-4 and see if the calculations are different.
If you did have excess federal withholding, you will get it back as part of your refund at the end of the year. To get it back early is possible depending on how flexible and intelligent your employer's accountant is.
