Can an employer not give benefitsto workers if they work over 30 hours?

These are two very different issues:

1) Can an employer not give benefits to employees who work over 30 hours? It depends. An employer does not have to provide ANY benefits--there is no law requiring health insurance, vacation, sick days, etc. If the employer does choose to provide benefits, it can define the rules to get them--e..g work at least 35 hours; only employees who've been there a year or more; etc. The only requirement is that whatever rule is set up must be applied fairly and consistely, so if other workers who work the same amount as you get benefits, it would seem you need to get them, too.

2) If the employee is not exempt from overtime, he or she must be paid overtime (time-and-a-half) for all hours worked past 40 hours in a single workweek. But if the employee is exempt, he or she does not have to get overtime. The Department of Labor, on its website, has the criteria for exemption; you should take a look and see how they apply to you. In brief, if you are hourly, you are definitely eligible for overtime. If you are salaried, you may, however, be exempt, if you a manager or executive; an administrative employee with alot of discretion or authority; a creative or learned professional (e.g. an art director or accountant); or in certain sales jobs.