Where would I record the employer payroll tax amount. The BS as a Liability, or IS as an expense?

It could be both statements. For sure payroll taxes are an expense ccount. If the tax is payable, which means that it has not been paid yet, then it would be on the balance sheet as well.

Right when you do payroll you are not actually paying the taxes at that time so the entry would be to:

Debt a Payroll Tax Expense account

Credit a Payroll Tax Liability Expense account