Just wanted to add to the previous solution. First, as previously stated in other Netflix solutions you DO NOT need to watch anything to get this achievement. You simply need to open the app. I went into my Netflix profile to be safe and just scrolled up and down.
More importantly I wanted to add that the best way, in my opinion, to view your progress and to make sure that your day registered is to double click the Xbox Guide button, scroll all the way down to "Snap an app," and select Achievements to view your Netflix achievements (On a side note this is the best way to check any achievement progress for any app). If you do not see any progression for the day, exit Netflix by pressing the Xbox Guide button and then the Start button and selecting "Quit." Try signing out of your Gamertag and repeating the process. Sometimes it doesn't seem to register. You can continue trying or try later in the day. You may also want to restart your Xbox.
I also see that a lot of gamers have been arguing in regards to the time that you access Netflix. While using my method I tried different times of the day. Sometimes 6am before I went to work, other times 7pm when I got back. There have been times where I registered a day at 7pm and then I try at 1am (4 hours later) and I register another day which debunks the having to wait 24 hours period. Therefore I personally do not think the time that you access the app necessarily matters because I was able to register a day during all different times of the day however I do acknowledge that sometimes you have problems registering a day and you have to try later.
**** Lastly I want to note that a few days ago I tried at 6 am and I was unable to register the day. I went out after work so I did not get back home until 3am the next day. I went into Netflix to check my achievement progress and I noticed that the day ended up registering anyhow. So I guess even if you don't see it register it still counts. I would keep trying until you see it register anyhow to be safe.****