I recently shifted from full-time (exempt salaried with full benefits--40 hrs/wk) to half-time (20 hrs/wk) with no benefits. My HR rep told me that I cannot work more than 1200 hours in a given year as a part-time employee, because if I work more than that, the company is obligated to allow me to participate in 401(k), and that I would have to be offered benefits (health care, life insurance, paid time off, holidays). Is there indeed a "magic" number of hours that turns a part-time employee into a full-time employee? I would really like to work 30 hours/week instead of 20.

The "magic number" is whatever the plan rules (and each plan can be different) say it is.

Additionally, the employer does not need to schedule you for the number of hours you want to work; he only needs to schedule you for the number of hours he wants you to work.

Agreed with the other answers, but I would like to pick a nit here. The OP mentioned 401(k), then mentioned "benefits". While all 401(k) plans are benefits, not all benefit plans are 401(k). A 401(K) is a very specific type of benefit plan subject to the ERISA law which has a mandatory plan on file with the government, which the government periodically audits and seriously penalizes the employer for any violations.

What is true for a 401(k) plan is very likely not true all other benefits offered by your company. Most benefits are not subject to the ERISA law. If you are looking for some one-size-fits-all answer that says any employee who works more then XX hours per week gets benefits, then no such rule exists. Each benefit not only stands alone, but is likely to very specific the company's specific plan/policy. You will need to check your company's benefit policies one benefit at a time to find out the rules for that particular benefit. And most benefits do not even have a formal legal requirement that the policy even exists. Medical plan is the other common ERISA level benefit that should also have a formal written plan. Most other benefits do not generally have a governmentally imposed plan requirement, although there are some reasons for the employer to voluntarily have a plan or policy anyhow.