Generally, the penalties for failure to timely pay license fees are fines, not jail. IF you look at the county's website, see what those fines are. You may also ask if there is any kind of amnesty program or a payment program for the past due fines.
Hope it works out for you - good luck!
Legal Disclaimer: You should remember that this answer does not constitute legal advice, and should not be relied on. This is because each state has different laws and each situation is fact specific. That is why a lawyer can't evaluate a legal problem without a consultation and a chance to review every fact and document at issue.
Also, this answer does not create an attorney-client relationship between us.
You'll need to contact the finance department of your county. You may also have city licensing and tax issues, so you'll have to contact them as well. There may exemptions for businesses as small as yours, or non-taxable years for new businesses, like there are in LA.
As my colleague noted, there could be CIVIL fines, but there won't be jail or any CRIMINAL penalty like jail.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.