The rule of law and tenth amendment mean that the federal government can't just do whatever the president wants. They have to be authorized specifically by Congress, and event then there are limits.
Congress, in the USA PATRIOT Improvement and Reauthorization Act, has said that the feds can ask for records, and can additionally forbid people to say that they have been asked. It doesn't say they can compel people to lie.
If the government orders them to do it, they can take the government to court, or they can just say no. The government then has to arrest them and try to convict them. Either way, a court would have to decide for sure. In this case, probably the Supreme Court, in that compelled speech has often been ruled as against the first amendment.
If the law that prevents you from telling someone you've received an NSL is considered not a violation of your right to free speech, I see no reason why it would be _more_ of a violation of your right to free speech for the government under the same law to require you to continue claiming you have not received an NSL.
After all, you had an easy way to not be in the position where the government is compelling you to say things -- you just could have not done the canary thing. Now that you're making a certain well-defined type of speech every week, the impact on your free speech rights to require you to continue to make that type of speech is pretty small, and I think you're in legally shaky grounds if you think that a judge or court would consider that much more of an impact on your free speech rights than the usual NSL gag order.
I agree that Congress could write a law that allows them to compel speech, and I agree that it might eventually be found constitutional. They didn't write that law, though, and speech that is both compelled and false is a different thing under the law than shutting up.
The government can't just order you to do whatever they like. That's what rule of law means. Nobody is obliged to obey someone's interpretation of the spirit of some law, just the letter.
Congress, in the USA PATRIOT Improvement and Reauthorization Act, has said that the feds can ask for records, and can additionally forbid people to say that they have been asked. It doesn't say they can compel people to lie.
If the government orders them to do it, they can take the government to court, or they can just say no. The government then has to arrest them and try to convict them. Either way, a court would have to decide for sure. In this case, probably the Supreme Court, in that compelled speech has often been ruled as against the first amendment.