H1B visas are for 3 years and extendible to 6 years. My guess is that a lot of relatively skilled Indian workers didn't want to return home when their visas expired. My experience with Indian coworkers a decade ago was somewhat mixed. There were a number of very skilled Indians, and there were quite a few that were pretty much worthless.
It might very well be in our best interest to extend permanent residency to the best of them, but we should ship the rest back home. Immigration can be very valuable to our country, but only when we are selective, and select wisely.
The number of undocumented Indians is dwarfed by the estimated 6.6 million illegal residents from Mexico, according to the estimates from homeland security's Office of Immigration Statistics.
I doubt that more than a tiny portion of them are undocumented. There aren't many Indians sneaking into the US. The come in through documented, legal ways, but they overstay their visas.
After 9/11 we became somewhat better at checking backgrounds on those that come here legally, so there is probably less of a security threat from those overstaying visas that from the undocumented immigrants that sneak across the border, or at least we know more about them.
Since the 9/11 hijackers did come here legally, and while we do better at checking than we did, checking background of people from some countries is nearly an act of futility, they do represent some risk. However, I think our limited resources are better focused on closing the border first and dealing with groups that have a higher percentage of criminal element.
What you have with an "illegal alien" is a visa jumper ~ may have come here as a student or tourist, or even as a diplomat, but overstayed his visa, or refused to go home because "things had changed".
Folks who never bothered to get a visa are, at best, undocumented tourists and should be treated the same as any tourist ~ sent home.
Just like everyone else, in other words.