Whose obligation is it to report the total amount of tips received and to pay the taxes owed by a waiter?

The employee is required give the employer written records of the total amount of tips that they receive during the month by the tenth of the following month.

The employer is responsible for all of the necessary required tax withholding amounts.

You can find the rest of the information for the below about tips by going to the IRS gov website and using the search box for Topic 761 - Tips -- Withholding and Reporting

Employees who receive tips of $20 or more in a calendar month while working for you, are required to report to you the total amount of tips they receive. They must give you written reports by the tenth of the following month. Employees who receive tips of less than $20 in a calendar month are not required to report their tips to you.

Employees must report to you cash tips received directly from customers, tips from other employees, and tips customers charge to their bills. Service charges added to a bill and paid to your employees are not considered tips for tax reporting purposes. These service charges constitute wages for purposes of social security, Medicare, and income taxes.

Employees can use Form 4070A, Employee's Daily Record of Tips, to keep a daily record of their tips and Form 4070, Employee's Report of Tips to Employer, to report their tips to you. Both of these forms are in Publication 1244 (PDF), Employee's Daily Record of Tips and Report to Employer.

When you receive the tip report from your employee, use it to figure the amount of social security, Medicare, and income taxes to withhold for the pay period on both wages and reported tips.

Self-employed persons If you receive tips as a self-employed person, you should report these tips as income on Schedule C or C-EZ. See Publication 334, Tax Guide for Small Business, for more information on reporting business income.

Reporting social security and Medicare taxes on tips not reported to your employer.

If you received $20 or more in cash and charge tips in a month from any one job and did not report all of those tips to your employer, you must report the social security and Medicare taxes on the unreported tips as additional tax on your return. To report these taxes, you must file a return even if you would not otherwise have to file. You must use Form 1040. (You cannot file Form 1040EZ or Form 1040A.)

Use Form 4137, Social Security and Medicare Tax on Unreported Tip Income, to figure these taxes. Enter the tax on line 57, Form 1040, and attach the Form 4137 to your return.

For more information go to the IRS gov website and use the search box for Publication 531 (2009), Reporting Tip Income