The government charges are set by the USCIS fee schedule for a petition or by CBP for a port-of-entry application, and licensing boards charge their own fees. Who pays them is a contract question between the nurse and the agency. Ask for the agency's cost allocation in writing before accepting.
Separate the government charges from the contract
Three sets of costs run alongside each other: licensing and credential verification, which the nurse usually pays and which occur first; the immigration application, whether a port-of-entry fee or a USCIS I-129 petition priced under the current fee schedule; and professional advice. Agencies differ on which they cover and whether they claw back costs if the nurse leaves early. Hypothetical example: a Lake Country nurse is offered a package where the agency pays the licensing fees but requires repayment if she resigns within twelve months; that clause is lawful in itself but should be read alongside the fact that her TN status is tied to that employer, so leaving early also means a new application.
Ask the agency for a schedule listing each fee, who pays it, when, and any repayment condition. Refer to the USCIS fee schedule for current government amounts rather than relying on figures quoted from memory by a recruiter.