In the last 10 years or so 37 points is the highest number which has still ended up in relegation, it's more normally around 34.
We really, really should be safe. But consider this: over the last 10 games we're 17th on form, joint with Everton in 18th. In the form table we are below teams we consider to be in the relegation fight like Ipswich and Wolves.
We shouldn't be panicking about it because it's so unlikely but we'd be foolish to just give up on the league entirely and concentrate only on the cups and just assume that there's nothing to play for. After the NLD we've got Everton - they're not great but they are scrapping away and they've lost less games than us. They'll sit in a low block while we just pass it around side to side and backwards, Everton will be content with a point but they'll still look to hit on the break. After that it's Leicester and that could really be an indicator.
TL;DR we're not in a relegation fight now but we will be if our players and manager don't snap out of whatever funk we've fallen into.