Which is correct?
There's a lot of people here today.
There are a lot of people here today.
A lot is a single entity. So is a few, a couple, a bunch, and a dozen. Because these words represent groups of items, many of us try to treat them as plural nouns. We'll say, "There are a lot of people here today," thinking that we've done the grammatically correct thing. We make grammar harder than it is.
This is really a very easy rule to apply. It's just a matter of realizing that words like lot, few, couple, bunch, dozen and others like them are singular. A lot. A few. A couple. A bunch. A dozen. The "A" gives it away. Treat these words just like you would treat the word "group," and you won't go wrong.
If you want to use a plural verb, that's fine. Just add an "s" to words like "lot" and, presto, we have a winner. "There are lots of people here today," is correct. Too easy.
I've tried to limit my use of the word "lot." "There's a lot of trees across the river," doesn't really tell you much, does it? How many trees are in a lot? I don't know. Except on eBay and at other auctions, not too many things actually come in "lots." Plus, you can dodge the whole singular vs. plural issue by using other words which are more descriptive and less vague. I'm certainly not suggesting that we start talking like poets or snobs, just that we try exercising our present vocabularies. Even a third-grader knows the word "hundred." "There are hundreds of trees across the river," tells me that we're probably talking about a forest and not a city park.