AJ's response, while not exactly incorrect, is decidedly incomplete and as a result is rather misleading.
To start with, just for the sake of completeness, at the present time only two states require that an employer provide health insurance at all. That will be changing in a few years but right now, unless you live in either MA or HI, health insurance is at the opt of your employer.
Having made the decision to offer health insurance, the employer then gets to decide whether he wants to offer it to all classes of employee, or only some. It is absolutely legal for an employer to decide to offer health insurance to full time employees but not part time; office employees but not shop employees; employees at the corporate headquarters but not employees in the branch offices; managers but not non-managers; executives but not non-executives; employees in Research and Development but not in Shipping; or any other class division that does not violate Title VII and related laws (race, religion, gender etc.).
However, once the employer has established which is or is not an eligible class, every employee in the eligible classes has to be offered the insurance. It is their opt to accept or decline, but it MUST be offered to all eligible employees.
All of the above, however, has to do with who must be offered insurance. It has nothing to do with whether the employer or the employee pays for it. The law does not address that issue, except to say that the employer cannot make such decisions on the basis of Title VII and related laws. Some employers pay more (or less) depending on the salary or the job position; other employers may use fully paid health insurance as a recruiting tool. This is legal. They simply can't decide that they'll pay the cost because the employee is black, or white, or male, or female, or Jewish, or Christian, or pregnant, and so on.