Millions of people work for the federal government, and millions more for state and local governments. Is there widespread corruption among them? I don't think so. And I don't think my countrymen think so either.
But "the government" is often meant as just the very top. The President is corrupt. Big swathes of Congress are corrupt. We have a Supreme Court justice more or less openly accepting bribes. Among that small group, I would be comfortable saying that corruption is widespread.
* for years people have noticed that many members of congress use privileged information to pick stocks.
* lobbying post-Citizen's United has a very decidedly "buying politicians" aspect to it
* a congressman (Menendez) was literally arrested while holding gold bars from a foreign government. he went to prison, but is the only person on this list who has iirc.
* the former mayor of new york (a long-time police offer) was embroiled in a Very Funny, very obviously true corruption scandal for turkish airline tickets. the prosecution against him was dropped for no good reason.
Or maybe soft bribery, like government officials being wined and dined by lobbyists. I'm sure that isn't "supposed" to happen, but I'm also pretty sure it happens a lot.
This sort of corruption exists a ton at corporations for sure, so I am hard pressed to think it doesn't happen in government