Not sure if you're talking about moving NATO troops around in the Ukraine, which isn't NATO, or moving troops around in a NATO country.
NATO has no responsibility to engage if the Russians invade Ukraine, but they may have to move assets to a NATO country that has a border with the Ukraine.
Going to be a hard sell to get Americans to get behind engaging in kinetic hostilities against Russia in the Ukraine, and without the US, NATO would be a speed bump for the Russians if they moved in.