No sponsorship is required for the spouses of those in E-1, E-2, E-3, and L-1 status, or spouses of those in H-1B status who are in the green card process and it's generally easy for companies to hire workers from the five countries with their own visas (Australia, Canada, Chile, Mexico, and Singapore). It's also generally easy for companies to hire those already in H-1B status - that is, to "transfer" the H-1B to their company. It's also generally easy for companies to hire those with PhDs (often via the O-1). It's also generally easy for companies to hire those in F-1 OPT and STEM OPT status but these workers will require sponsorship to continue working and this sponsorship usually takes the form of the H-1B visa, which requires going through the H-1B lottery, a very messy and uncertain program.