First off the etymology:
The word 'alien' has a legal definition. It's not derogatory. As defined by law.com as
>1) a person who is not a citizen of the country. 2) in the United States any person born in another country to parents who are not American and who has not become a naturalized citizen. There are resident aliens officially permitted to live in the country and illegal aliens who have sneaked into the country or stayed beyond the time allowed on a visa. 3) v. to convey title to property.
So what's the left's problem? What's the big fuss about? Leftists like illegal immigration and they want to use language to change public opinion. There's a huge difference in connotation between 'illegal alien' and 'undocumented immigrant.' What do you innately think of the words 'alien' and 'immigrant?' Aliens = bad. Immigrants = good. When you hear 'Illegal' you think the situation should be handled by law enforcement and there's a criminal element, which there is. When you think 'undocumented' you think it's just a clerical error that needs to be rectified.
The problem is, the left can't argue this point with logic and reason unless they want to quote people on the right like Milton Friedman. And they don't know who Milton Friedman is or they would be conservatives. So they use the only tool they have, uncontrolled emotional anger.
So use the term Illegal Alien. Don't back down from it. It -will- bait leftists in. I've seen many leftists get destroyed when they go after the terminology, simply because they don't know what words mean. It makes them look silly and ruins their credibility before they even attempt to make a flimsy emotional case for illegal immigration.