TN Visa

You don't need sponsorship for the TN, it's technically a status and not a visa. Instead of being stamped in as a visitor, you are stamped in with work privileges.

The first thing you will need to do is apply for your CGFNS visa screen certificate. Then you just need to apply for a job. The hospital or agency that hires you needs to give you a letter detailing your job description and requesting that you be admitted to the US on a TN status for X amount of time - they can request up to 3 years at a time (you can renew it again and again when it expires- there is no limit to how many times a TN is renewed). You take the visa screen certificate, the work letter, and your degree (no one has ever actually looked at mine, but the one time I didn't bring it he asked where it was!) to the immigration control officer and tell them "I would like to apply for a TN" and they will send you off to the secondary screening room to have everything processed.

Best thing is to tell companies that the TN is NOT a visa and they don't need to apply or petition for anything. You simply need a job offer letter that requests you be admitted to the US to work.