Unfortunately I can only read the abstract of the actual study but the article seems like crap. They state a bunch of opinions as fact. For example:
"Remember, a low-ball estimate says there are at least 11 million to 12 million illegals in the U.S., but that's based on faulty Census data. More likely estimates put the number at 20 million to 30 million."
What more likely estimates? What is your source? There are a number of different agencies and groups that estimate about the same numbers, some of whom have a vested interest in inflating the number (like the DHS). From Wikipedia:
The United States Department of Homeland Security (DHS) has estimated that 11.4 million unauthorized immigrants lived in the United States in January 2012. According to DHS estimates, "the number of illegal immigrants peaked around 12 million in 2007 and has gradually declined to closer to 11 million." The DHS estimate "is in the same ballpark as several independent organizations that study illegal immigration, including Pew Research Center (11.3 million); the Center for Migration Studies (11 million), which studies migration and promotes policies that safeguard the rights of migrants, and the Center for Immigration Studies, which advocates for low levels of legal immigration (11–12 million)."
"Specifically, the authors say that illegals may have cast as many as 2.8 million votes in 2008 and 2010. That's a lot of votes. And when you consider the population of illegal inhabitants has only grown since then, it's not unreasonable to suppose that their vote has, too."
The data from Pew indicates that the number has either stayed level or gone down (at least in the years they are citing). Again - what is your source of this data?
"Leftist get-out-the-vote groups openly urge noncitizens to vote during election time"
Which "leftist" groups? What did they say? This might have happened but it seems foolish just to take this on faith, extraordinary claims require extraordinary proof. I couldn't find too much relevant on Google (search terms "groups encouraging illegal voting california"), other than the claim (easily debunked) that Obama encouraged illegals to vote.
"Heck, even the liberal fact-checking site FactCheck.org says so."
What is your evidence that that the site is "liberal"? Is it just because they said something that disagrees with your narrative? According to their about page, We are a nonpartisan, nonprofit “consumer advocate” for voters that aims to reduce the level of deception and confusion in U.S. politics. and publicly list all sources of their funding here.
In summation, the article seems quite bogus with a number of seemingly false or unsourced claims. This is a great example of the biased news that the site seems to rail against, but only if they are biased to the left.