It's actually been a while since I've heard people talk of push communication, so maybe I'm a day late and a dollar short on this, but I can't help when I have my epiphanies.
The idea behind push communication (when I heard it, at least) is that instead of waiting for users to come to your website for news, you could push it out to them through, for example, an RSS feed.
Hands up those of you who, when you ask your users to put their hands up if they use an RSS reader, ever get anyone putting a hand up? No, nor do I. And this is the problem: if you're pushing information out to somewhere that people don't visit, you're still asking them to pull it.
Even if you push it right to their email inbox, if they only check their email when their kids mention they've sent photos of their grandkids; or if you're pushing it to their student email account and they only ever check their dotcom-mail if that; you're still not going to be successful.
My phone company pushed an SMS message to my cellphone on the 28th July to say that my account's going to expire next year, my terms and conditions have changed, and I can get a new phone on some special offer until the 31st July. I finally noticed this message on the evening of the 31st July.
I only listen to the radio in the aftermath of natural disasters. I have friends who (by choice) don't even own a TV (I use mine so rarely I forget which buttons on the remote to press). There's no guaranteed way to push your communication to all your users short of accosting them face-to-face, and even then, even if you offer candy, a measurable proportion will still avert their eyes and walk right past you.
Of course RSS is still a handy tool, because it lets you embed the feed in places where hopefully the users will go. We embed ours on the library homepage, some subject guides, and our Facebook page. But that just gets more users, not all. (The most common response when I tell students about our Facebook page is laughter. Sure we've got 900+ followers. But that leaves probably 18,000+ non-followers.) We can communicate all we like through these channels, but the majority of our users -- even when they're motivated to find out which buildings are open to be borrowed from/returned to this week -- still don't know what's going on in the library until they get a library tutorial. (And in the last few weeks the attendance rate at my tutorials is running at about 2/3.)
Long story short, if you want a message to get to all or even most of your users, you're going to have to push hard and you're going to have to push really really smart.