The lady said she was from the National Healthcare Service and asked if I had health insurance. I said "you realize you're calling a business right?" She said "No I did not" and hung up.

"Missed Call" guessing it's healthcare.

I set up a Healthcare.gov account a year ago, going into 2015, and they got the number from there.

I never requested healthcare quotes.  They are getting the number from healthcare.gov.

These people pop up on my caller ID as "National Enroll..." which is some crap about healthcare. National Enrollment Services, specifically. They have called from this number and 14 other numbers in two days time, repeatedly, despite every number being blocked. I've been nice, I've been nasty, I've ignored the calls and they still do not stop, they just find another phone number with a different area code and exchange to call from. I'm ready to get rid of my phone.

November 1 is the start of enrollment periods for new plans that begin on Jan 1st.  For all kinds of employers, and I am pretty sure for US Government and State employees.  And for those covered under obamacare.  I think you can expect more calls.