Close Encounters was released a few years after the Watergate scandal, a series of political scandals that resulted in the impeachment and resignation of President Richard Nixon in 1973. One of the results of Watergate was a sweeping distrust of government.
Of course, this isn't to say that all Americans have ever been huge fans of the feds. Conspiracy theories are as American as apple pie and combining the names of celebrity couples into stupid catchphrases. It's just what we do in between football seasons (sorry baseball, but we all know it's true). To pick just one of many possible examples, the Roswell Landing conspiracy dates back to 1947.
Since the film contains both aliens and government functionaries, a conspiracy is bound to exist; that part of the story writes itself. What's more surprising is the way the government is treated, at least according to some analysts.
Professor J.P. Telotte doesn't think the government is presented as a Big Brother-type organization, hiding reality under a web of lies to further the interests of its members. Instead, it's "a kind of protective parent: determining what we should know; trying to insulate us from any disturbing and thus potentially dangerous revelations." (Source)
Take Major Walsh, for example. His people make up the story of the chemical spill, a story he characterizes as "something so scary, it'll clear 300 square miles of every living Christian soul." His goal isn't to use force. Instead, he creates the story to get the people to work with, not against, him.
That's one way of looking at it. Another way is that the government lies to its citizens about the most important event in the history of mankind. We get that they don't want anyone to get hurt—those aliens might be of the Mars Attacks! or Independence Day variety as far as anyone knows. And can you imagine the panic and chaos if Wolf Blitzer announced an alien invasion on CNN? What would you do? Oh, right. You'd be watching reruns of "The Bachelor," so you wouldn't hear the announcement.
Still, it's a massive cover-up. In a movie about the benefits of childlike wonder and seeking the truth, the government's cover-up, even if it's for the people's own good, becomes antagonistic from Roy's perspective as a truth-seeker.
In the final analysis, we think the government handles things pretty intelligently. They don't nuke the mother ship. They understand that something significant is about to happen, they gather their scientific and technical resources and personnel, and they're cautious but open-minded. Calm and intelligent minds are on the job to manage the close encounter, and they're almost gleeful once things get going—they welcome the scientific discoveries. They outfit some human ambassadors to send on their way to galaxies far, far away. (What's in those duffel bags?)
Then maybe they call Wolf Blitzer.