No, not at all. They have all the time in the world. Just be wishy washy and lie until this loses the public interest. Nothing changes, and you go back to what you're doing. The US Congress and POTUS have indicated that they have absolutely no intention of changing the status quo. That lying to them is fine, if you do so in the name of "intelligence gathering" or "fighting terror".
So I have to disagree. A lack of steam is not their problem. The only thing they have to fear is public outrage, which has never reached very high on this.
If the copyright hadn't expired long long long after the majority of people are interested, those works might be getting a great deal more attention. How many people who saw them in the theater are still alive today?
You know the old adage "never attribute to malice that which is adequately explained by stupidity"? I think an appropriate addendum would be "never attribute to ignorance that which is adequately explained as paid rhetoric."
A long time ago, they passed a law preventing movie studios from owning theaters as it was unfair; movie theaters were essentially the only place to see art of this nature, and studios could (and did) limit shows to films they produced.
I've been thinking that law is obsolete for some time, but perhaps it really just needs to be expanded to include ISPs. Perhaps it should be illegal to be a content provider and an internet service provider, as companies cannot be trusted to treat other content providers fairly.