That's per dyno, per second. 6,000 per dyno total, which seems very reasonable. As timdorr mentioned, Pusher's largest (publicly available?) plan only allows for 5,000 connections.

We run http://firehose.io/ on smaller SoftLayer metal servers and get around 10k connections per box. These servers cost $250 per month, so we get about 20k connections for $500 per month. By my back of napkin numbers Heroku is about 10x the cost of real metal servers.

I ran a quick test, an entry-level box from Digital Ocean can sustain 350+ connections/sec and maxes out at around 7,200 open connections.

Having root access to the machine would allow you to optimise some things and probably raise those numbers, but then you don't get the convenience of using Heroku.