Guys, an FBI investigation is pointless. This is something that happened 36 years ago. The woman involved is admittedly sketchy on details. The people she can name have all given sworn statements that they have no memory of any of the events she described. Gathering any useful evidence on a case like this is pretty much impossible and, honestly, every Democrat who screamed about an FBI investigation yesterday knew it was useless.
So why are the Dems asking for an investigation? A couple reasons. The biggest reason is they want to stall. Stalling this gives them a big issue to rile up their base in the election. Additionally, the Democrats still have hopes of retaking the Senate in November (though they wouldn't come into power until January). If they can delay the Kavanaugh vote for another 6 weeks, it would not give the Republicans much time to ram though a candidate if Kavanaugh fails. The Dems, knowing the investigation will turn up nothing, know that these accusations will still hang over Kavanaugh's head after the investigation. If they can delay the vote, win back the senate, and defeat Kavanaugh in the lame duck session, there probably wouldn't be enough time for another candidate and the Dems would then hold that seat open for 2 years.
It's a long shot for all that to happen but it's honestly the Democrat's best chance to keep the court from swinging to the right.
The second reason they demand an FBI investigation is optics. They want to put the Republicans and Kavanaugh between a rock and a hard place. If the Republicans refuse an FBI investigation, they'll look (to gullible people) like they're trying to cover something up. If they give into the investigation, they play into the Democrat's game. With Kavanaugh it's even more clear. If he came out and demanded an FBI investigation (something I doubt he fears), he alienates Republicans who might just decide to kill his nomination now. If he says there shouldn't be an investigation, it looks like he's hiding something.
It's a fairly masterful job by the Democrats.
The Republicans are not going to play ball though. They're going to push ahead with the vote whether Kavanaugh will be confirmed or not. The Republicans know they have to resolve Kavanaugh quickly in order to ensure they have a second chance if Kavanaugh isn't confirmed. If they keep the Senate in November then they have all the time in the world but they can't rely on that at this point.