How do I change the "Liability Period" on my upcoming 941 payment? Shouldn't it match the pay period?

It has nothing to do with your pay period, well little. You are either monthly or semi weekly. 

Monthly Depositor

Under the monthly deposit schedule, deposit employment taxes on payments made during a month by the 15^th day of the following month. Employers who deposit monthly should only report their deposits quarterly or annually by filing Form 941 or Form 944.

Semi-weekly Depositor

Under the semiweekly deposit schedule, deposit employment taxes for payments made on Wednesday, Thursday, and/or Friday by the following Wednesday. Deposit taxes for payments made on Saturday, Sunday, Monday, and/or Tuesday by the following Friday. Report your deposits quarterly or annually only by filing Form 941 or Form 944.