There's no limit. A merchant is entitled to restrict payment methods---apartments often don't accept cash in payment of rent, and fast-food joints won't take bills larger than $20---but as far as I can tell, your way to legendary status as a pain in the IRS's neck is clear.
The Internal Revenue Manual
Part 21 - Customer Account Services
Chapter 3 - Taxpayer Contacts
Section 4 - Field Assistance
"1. The IRS must accept cash payments from taxpayers who do not have a check or money order, are unable to obtain one, or insist on paying in cash."
This is followed by
"Procedures For Accepting Cash Payments
"1. General procedures for accepting cash payments are:
"A.Ensure that the taxpayer has the exact amount of the payment. DO NOT MAKE CHANGE.
"B. Count the cash carefully in the taxpayer's presence..."
P.S. Here are some brothers in arms:
Court settlement paid in pennies
Rusty Wallace once paid a fine (for swearing) in pennies
Parking ticket paid in pennies