H-1B visa sponsorship is required for any foreign national who wishes to work in the United States beyond the requirements of their student visa. While there are other types of visas, this is the most common type of sponsorship.
There is a limited number of H-1B visas issued each year.
Most any employer can offer you H-1B sponsorship. However, many will resist it because it is either perceived as too expensive, or they simply do not know what steps they need to take to do it.
To learn more about visas and work authorization in the U.S., visit the ISSS website.