Long term? Minimal. All the niches it fills, have alternatives that would just grow to fill them in.
Short term? Catastrophic. Losing GMail and "login with Google" would leave a lot of people with no email, no way to login to other services, and no way to recover their passwords (through email). The loss of Photo backups would also upset many, Drive and Docs would leave a lot of people and businesses without their daily tools. Search would likely be the less affected, with plenty of alternatives already to pick from.
More catastrophic than any of that would be the loss of Google Cloud Platform. A huge amount of the Internet runs on Google cloud platform, millions of businesses, even Spotify and Twitter are hosted on Google cloud platform. So unless they have a hybrid-cloud strategy, which I can guarantee for 99.99999% they do not, then a huge section of the Internet and business in general goes down.
Buying the government (if doing so was even possible) means they need to furnish it's debts.
Even if a company was willing to to undertake such a burden, nobody makes more money than the government, it just doesn't have much reason to hold onto any of the cash it collects.
I don't think a company as big as Google could die without a couple months notice. I think most companies would go to special lengths to get their users to setup alternatives. Gmail accounts would get flooded with "hey since Gmail is going away don't forget to change your login preferences, we'll force you to add a new email next time you login". And there would be a massive number of memes like when gpdr took effect.
It would certainly be a chaotic and annoying time, but I think most vital services wouldn't be so bad and Microsoft would grab a nice little monopoly on office apps again.
I think it is unlikely that they would do down without selling there users. So Gmail would become Hotmail, Google drive would become Dropbox and so on.
When I read the post I was initially focused on google search but man….if gmail were to die, the pile-on effects would be seriously catastrophic and it would take a very long time for things to stabilize again. It’s not just personal emails that are handled by gmail - their corporate offerings are used by a ton of companies, and there are plenty of school districts as well that rely on it for their email (and thus associated logins). If you’ve ever worked near education, you know what a cluster that would be as all the IT departments scrambled to figure out who would be responsible for a migration.
I don’t really see it happening, but it’s very scary to think about what would happen if gmail were to fall.