Who's Against Illegal Immigration?

Everyone, at one time or another.  Even Democrats, if the timing is right.  There was a time when Americans agreed that illegal immigration was bad, now apparently only Republicans do:

All Americans, not only in the States most heavily affected but in every place in this country, are rightly disturbed by the large numbers of illegal aliens entering our country. The jobs they hold might otherwise be held by citizens or legal immigrants. The public service they use impose burdens on our taxpayers. That's why our administration has moved aggressively to secure our borders more by hiring a record number of new border guards, by deporting twice as many criminal aliens as ever before, by cracking down on illegal hiring, by barring welfare benefits to illegal aliens. In the budget I will present to you, we will try to do more to speed the deportation of illegal aliens who are arrested for crimes, to better identify illegal aliens in the workplace as recommended by the commission headed by former Congresswoman Barbara Jordan. We are a nation of immigrants. But we are also a nation of laws. It is wrong and ultimately self-defeating for a nation of immigrants to permit the kind of abuse of our immigration laws we have seen in recent years, and we must do more to stop it.

--President Clinton's 1995 State of the Union Address

Democrats remember that we are a nation of immigrants. We recognize the extraordinary contribution of immigrants to America throughout our history... Today's Democratic Party also believes we must remain a nation of laws. We cannot tolerate illegal immigration and we must stop it...

--1996 Democratic Party Platform 

And here's a couple videos.  When I find more, I'll post them.