I don't think they are against that authority - I think they are against how that authority is being used.
Clearly, the law needs to be changed (again) to avoid abuse of that authority.
In September, 2001, George W. Bush, Declared a National Emergency by Reason of Certain Terrorist Attacks. That declaration is still in effect. I would say that Trumps declaration of a national emergency is very similar.
Again, the big difference I believe is Trump asking for $$ and then when denied, declaring a national emergency.
He should have never shut the government down. He shouldn't have brought the media in and challenged Nancy and Chuckie.
He should have announced that caravans were arriving, things were getting out of control at the border and declared a national emergency, sent in the military and asked for $. He could have had the military build the wall. He went about things backasswards.