Possibly, but not on the free tier. Anyway, our current plan can only handle 20 concurrent connections to Postgres and I am not planning to pay more to satisfy spikes.
Can you clarify on why not? If you get interest and a big news hit, isn't it important to you to capitalize on that as much as possible and leave a good impression so people come back to use your service?
If you don't have the funds that's one thing and I get it, but seems like spikes are exactly the kind of thing worth spending on.
The website a weekend project, not something I care for whether people use it. On average it has five to ten visitors a day unless linked to from somewhere big which only happens like twice a year.
From my impression, I don't think it's any kind of for-profit service he's running where people are paying for and expecting uptime. He's taken a public data source and make it very easy for people to peruse it, and sees that as his reward.
Heroku doesn't automatically scale it for you, though you have the ability to increase the number of dynos. There are services that will do that for you, but it's probably better that you have to explicitly scale so you don't get hit with a sizable bill you weren't expecting.
In any case, there are other constraints than just the amount of webservers that could be causing the outage e.g. the database.
They are fixing it!