First off, getting a bunch of upvotes does not make you a mod. Being a moderator has not too much relation with rep-- just `cos you have a bunch of rep doesn't mean that you are a good mod candidate.
That being said, at 10k and 20k rep, you do get access to quite a few moderator tools. These reduce the burden on the diamond mods, but you're not compelled to use them. On the other hand, diamond mods keep their modship only if they are active (I'll loof for a reference for this.)
Mods are elected by the community. While rep is a rough metric, mods aren't elected just on the basis of rep. Check out SO's mods (scroll down). Their rep varies wildly, ad we have tons of higher-reps. In fact, the only high-rep on that page(the first two pages) with mod powers is Marc Gravell. And he's an SE employee (though I hear he got the diamond via the normal route as well)
This is what we look for in good mods. Not rep. Other moderation qualities.
OK. Back to the question. Not being a mod myself, I don't know--but you only need to give 1-2 hours a day for moderating. If you and your fellow mods on a site are good, then you really need not actively spend time. Keep an X.SE tab open and keep an eye on the tools popup/new questions. If you see something new, take a look at it. On larger sites, I guess the mods don't really look at new questions but rely on the other folks online to comment on them for improving/may be closed. And, of course, we have the flag system so even the guys with 1 rep can bring something to the attention of the mods.
Note that as a site gets larger, new mods are elected every year (Only if it's necessary). So the workload evens out. And of course, the more 20ks you get, the easier it is to moderate.
Interesting read: Who are the diamond moderators, and what is their role? (Thanks, @Yannis, for making me have to not search for this)
Being a mod isn't a primary occupation--SE doesn't pay them{*}. It's completely a volunteer job. You volunteer for the elections, and the community chooses you.
*Except for SE Inc. employees--but they're not really mods(as in, they're not expected to moderate; though they do help out in this department on betas). They have the diamond and mod-ninja powers, though