

If they had something to fight for, I think they would.
In reality, they have Maduro (who has suppressed a popular uprising against himself, and likely didn’t win the last elections) and 20% of inflation per month.
If the US does attack, predictably, only hardcore fans of Maduro will oppose. But the force that Trump has sent is not capable of occupying Venezuela, only striking it and incapacitating the government.
But an attack is an attack - if Trump does order an attack, I have free real estate to sell him… in the Hague, because international agression is prohibited.
Personal suspicion: maybe in Alaska, one man told another: “you can get Ukraine” - “and you can get Venezuela”. One of the men may think he’ll get Caracas in 3 days and will be met with flowers. The other guy may hope that Caracas looks like Kyiv, which he’s been “getting” already for 3 years. But I doubt if Caracas looks like that.
Regardless of what will happen, the story about narco-terrorism is hot air. Smuggling is not war. Smugglers can and should be arrested, not bombed with drones. If this becomes a cause for war, then war will be based on fiction and lies.

If the acting president wants, supposedly yes. Emperor Bush II made it thusly, upon going into Iraq for the second time, this time based on lies (and resultingly, starting up ISIS).
(Note: president Bush I had gone into Iraq based on a valid UN resolution due to Iraqi agression.)
https://en.wikipedia.org/wiki/American_Service-Members'_Protection_Act