Is a short term note payable a liability?

All payable accounts are liabilities regardless of them being short term or long term.

A liability is ANYTHING a company owes. The only exception to this rule is generally everyday expenses incurred by the company and/or business. Expenses such as Wages, Salaries, Utilities, Rent, ETC. These too can also become a "liability" if payment is delayed.

For example, you owe John Q, $1500 in wages but will not be paying it until the next accounting period, you still have to put it in your books, therefore you will list it as Wages Payable - John Q (credit) $1500 & Wage Expense- John Q (debit) $1500. Because you have NOT paid this but still "owe" it, the Wage Payable becomes a Liability for the company until it is paid off. Once it is paid off you Debit the Wage Payable account (to bring the balance to $0) and Credit your Cash account for the amount paid.