You say: "we're a little tight on fuel..." or "we're fuel critical.." What does that mean exactly? The controllers want to know how long can you continue to fly. That seems to be the best way to understand the situation.
What I can't understand is how anyone can have less the 45 minutes & they're not on their way to their alternate
Certain languages [sometimes] do not translate well....BUT.
IF you have a fuel problem, you tell ATC
A.S.A.P.
But how [without the say so of ATC] are you going to get to your Alternate?