No, but we do have universal healthcare. The Netherlands actually used to have something like a public option about 10 years ago (2/3rds was covered by public insurance, the rest had private insurance). But in 2005 or 2006 the government decided to ditch it. The results are hotly debated. Healthcare has become more expensive than 10 years ago and the bureaucracy still is terrible, but waiting lists are much shorter than under the public option. And because wealthy people could afford private insurance they had access to much better care (the disparity is smaller now). The costs of the public option also were projected to explode. Personally I strongly oppose returning to a public option and I think partially privatizing healthcare has been a succes, but it's hotly debated.
Implementing single-payer would be nearly impossible though. It would cost the government a lot of money, and they would need to buy the insurers out. Another reason why Jan-Peter Balkenende is the most underrated Dutch PM ever
. I start liking Balkenende more and more. Everyone always says that Piet de Jong is the most underrated Dutch PM ever, but that meme is so overused that he's probably overrated by now.