All I can find on the Smithsonian is that they did press interviews, where various staff expressed opposition, and that they also sent some report to Congress. The press interviews are, quite naturally, public statements, and it could be argued they're unrelated to lobbying. As for the report, that's part of their normal duties - it would be a real catch-22 if such a report were considered lobbying. This feels like bluster from the politicians; they write dumb letters all the time for PR purposes.
The space shuttle situation, though, is a disaster.
Strangely, according to its Congressional proponents, the language in the bill says "to transfer a space vehicle involved in the Commercial Crew Program". That would not be a Shuttle. That's a Space-X Dragon, or one of the boosters.
The remaining Shuttles were delivered by carrying them atop NASA's Shuttle Carrier, a Boeing 747 rigged for that, and landing it at a nearby airport. Those craft were retired years ago. Unclear how to move the thing without cutting it apart.
The space shuttle is fine where it is. Why does it need to be moved now?
The bill allocates $85 million to move the shuttle. For some reason Senator Cornyn doesn't mention that number in his press releases. The relevant text:
> (F) $85,000,000 shall be obligated to carry out subsection (b), of which not less than $5,000,000 shall be obligated for the transportation of the space vehicle described in that subsection, with the remainder transferred not later than the date that is 18 months after the date of the enactment of this section to the entity designated under that subsection, for the purpose of construction of a facility to house the space vehicle referred to in that subsection.
Also, the Air and Space Museum is free and Space Center Houston (the new location) charges $30 per person.