This story is starting to look like just a case of panic.
This CNN article is one of the most skeptical. It makes the point that one of the people who was bitten was probably actually bitten by a poisonous snake. It also adds that the man was not taken to a Western hospital for treatment, but instead was brought to a local healer or shaman for assistance. (There are a lot of illnesses where faith healing can be useful - the placebo effect is surprisingly strong. But I don't think "snake bite" is one of them.)
The article also cites a reporter who believes the second person wasn't bitten by anything.
About 20 people have sought medical assistance for spider bites in the northern Indian town of Sadiya in the last two weeks. Only a few of them were confirmed as having been bitten by a spider, and most of them were bitten by known local species. I read another report somewhere that one spider bite a week requiring hospitalization is about normal for this part of the world, in this time of the year.
It appears that the spider panic began locally, and has been spread online. The rumor is that the town's festival ended with a panic involving a swarm of biting spiders of an unknown species. And yet we have no photographs of this swarm, and no confirmed reports of anything other than normal spider species present in normal numbers.
There are no native species in Assam which are venomous, although there are many spiders that can give you a scare. It's possible that an introduced species has overtaken the small town of Sadiya, although no unusual species have been collected yet. Speculation that this could be the work of Australian funnel web or black wishbone spiders is entirely fantasy at this point.
People have reported that the large spiders are quite aggressive, some have claimed that the spiders leaped at them and latched on to bite. Unlikely though it all may sound, panicked district officials are giving serious consideration to spraying the entire town with DDT. Let's hope it doesn't come to that; Sadiya is certainly home to millions of innocent if not helpful insects, and the repercussions to local wildlife could be severe.