How many people are illegally present in the United States today? Nobody knows the exact answer of course, but the best estimates from the Pew Center (through 2014) puts the number at roughly 11.3 million people. One important subsidiary question for which (up until now) we have had no real data at all is how exactly those who are illegally in the United States came to be here. At the risk of simplifying the question there are two basic answers to that question: Either they entered the United States illegally in the first instance (e.g. by crossing the border) OR they entered the United States legally (on a visa permitting entry or on visa-free status) and then remained in the United States past the time when their authorization to remain here had expired. For ease of discussion we call this later category "visa overstays."
What the percentage is of each group may very well drive your investment in enforcement and investigation. If, for example, you thought that illegally entry was the dominant problem, you might build a wall. By contrast, if you think visa overstays are the source of illegal presence you might invest in a system of entry/exit registration to track people who lawfully enter and ensure that they leave in a timely fashion. Both are expensive propositions (unless you get someone to pay for building the wall) and, given finite resources, are often seen as competing claims on scare dollars and attention.
The problem however is that up until now nobody has any real handle on what percentage of the illegally present were visa overstays and what percent were illegal entrants. Now, however, DHS has released the very first bit of summary data on what the level of visa overstay is in the US. According to DHS, last year roughly 45 million people arrived in the US on a visa (or in a visa-free travel system). Of those, they estimate that 416,500 were still in the US at years end past the expiration of their visa.
1) This involves only air and sea arrivals. We have no data for land border crossings at all. [Imagine the lines if we had exit screening at the land border!];
2) That really, really skews the data. As Pew Center puts it: "Mexicans made up 49% of unauthorized immigrants in 2014 (including some who arrived decades ago), but according to the report, they account for only about 9% of foreigners (or 42,000 people) who arrived by air and sea, overstayed and had not left by the end of fiscal 2015. Canadians, meanwhile, account for about 1% of unauthorized immigrants in Pew Research Center’s latest estimate for 2012, but 19% of overstayers who had not departed by the end of fiscal 2015, or 93,000 people."
3) Nonetheless, the data are strongly suggestive that visa overstays are not the problem with illegal presence. A default rate of roughly 1% is, to be candid, shockingly small. If you had asked me to guess before I saw this I might have said something on the order of 5-10% for overstays.
4) On the other hand we really don't know the other number -- how many enter illegally across the border. We do know that Customs and Border Protection is making 500-600,000 apprehensions annually, and deportations are of the same rough order of magnitude. But nobody knows how many cross the border and are no apprenended (though we also do know that the flow is decreasing in recent years).
All in all, the new data from DHS serves as modest support for my own personal instinct (and it is nothing more than that) that visa overstays are less of contributing factor to illegal presence than illegal entrants -- probably by a factor of 5. But that's just a guess.