Whenever there's a partial shutdown of the federal government -- or even discussion of cutting government budgets, including at the state and local levels -- politicians often follow the "Fireman First Principle", described by Mickey Kaus this way:
a clever bureaucrat, faced with a budget reduction, will threaten to cut not the least essential services but the most essential (in order to provoke public outrage that results in the budget reduction getting cancelled)
In other words, if you're a mayor who wants to scare the citizenry out of their demand that you stop wasting their tax money, you say that any budget cuts would mean firemen and police would have to be furloughed, rather than laying off, say, the deputy diversity coordinator of the water and sewer department.
There's a limit to how far the Obama administration can follow the Fireman First Principle in immigration. Its hostility to keeping out illegal aliens is offset by the vital national security role of border inspectors and Border Patrol agents, whose absence would result in a disaster that no amount of White House PR spin could pin on the opposing party.
That's why border control operations are not discontinued by the "shutdown". Nor is the handing out of green cards, since most USCIS functions are funded by fees paid by applicants rather than congressional appropriations. See here and here for more on how the "shutdown" affects immigration functions.
But the one major immigration function that the Obama administration has suspended pending a resolution of the budget impasse is E-Verify, the online system that checks the employment eligibility of new hires. It's hard to see this is anything but intentional -- the administration is deeply hostile to anything that makes life harder for illegal aliens; E-Verify, even in its current state as a voluntary system, is used to screen some one-third of new hires nationwide, complicating efforts by illegal aliens to get work.
But E-Verify is an automated system, with almost all replies untouched by human hands. The administration could have discontinued just the manual confirmations required in a small percentage of cases, but instead have shut the whole thing down.
This despite the fact that other automated, web-based functions continue to work. For instance, I just subscribed to DHS's e-mail lists with one of my backup e-mail addresses, and had no problems; I even received e-mail confirmation from DHS. So that's an "essential" function but the automated functions of E-Verify are not?