Can I reasonably expect a USB connection manage a 3.7 Volt 6-8 Watt output at 1.9 Amps or less?
I don't have the faintest idea what an "510 Vape eCig mod" is (glow plug model car??).

But NO, from you specs this is not something you can expect an USB connection to do for you, because


An USB host is not required to provide more than a minimal amount of current untill the connected slave negotiates for more;
An USB host is not required limit the current that it supplies beyond "keeping it at a safe level", which seems to be interpreted as "when the USB host does not explode it is OK".


This might seem contradictory, but it is the freedom the USB specs allow.

To summarize: The USB host is free to provide either to little or too much current for your purpose.