The Constitution specifically empowers Congress to suspend the writ, as follows:
"The privilege of the writ of habeas corpus shall not be suspended, unless when in cases of rebellion or invasion the public safety may require it."I suppose one can argue over whether it is appropriate in this case --- I might even agree with them --- but let's not pretend that even suggesting it is unconstitutional. Or that its scope is broader than it is. One incredibly foolish group is even suggesting that it "could allow the government to detain the attorneys themselves as 'enemy combatants.'"
One frequently wonders what color the sky is on the planet of these lunatics. Apparently, too, they speak another language. Clearly, they don't understand English.