Gary Illyes from Google said at the BrightonSEO conference that those with responsive sites don’t really need to worry about the upcoming mobile first index. I was not at the event where he said that but Greg Gifford was there and he posted it on Twitter.
He said:

if you have a responsive site, you don’t really need to worry about the mobile first index@methode #brightonseo
— Greg Gifford (@GregGifford) September 15, 2017
Google has been proactively encouraging webmasters to get their sites ready by migrating to responsive design. The mobile first index is expected to happen sooner than later and the best way to do that is to make sure your pages are equivalent and responsive sites help with that.
So if you want to feel somewhat safe, go responsive. Otherwise, check page by page to make sure your pages are equivalent.
Forum discussion at Twitter.
This post was scheduled to go live today but was written earlier – I am currently offline today.