Well, both government cuts and cracking down in illegals coming across the border have been reiterated throughout several of his interviews and speeches. Here is a bit on both, I suggest reading the full links... all are excellent information on his positions in these areas.
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REGARDING CUTS:
"Arnold Schwarzenegger's top fiscal adviser says he is drawing up several budget options that would avoid new taxes while imposing spending cuts that he insists won't cause widespread hardship."
"John Cogan, the conservative Stanford University economist who also drafted George W. Bush's tax cut proposal during the 2000 presidential campaign, said in an interview that the cutbacks needed to wipe out California's budget deficit would still leave spending significantly higher than in 1999."
http://www.freerepublic.com/focus/f-news/982393/posts .
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"We must immediately attack the operating deficit head-on. Now does this mean that we are going to make cuts? Yes. Does this mean education is on the table? No. Does this mean that I am willing to raise taxes? No. Additional taxes are the last burden that we need to put on the backs of the citizens and businesses of California."
http://www.freerepublic.com/focus/news/975930/posts?page=34 .
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REGARDING CLOSING BORDERS
LOS ANGELES (Reuters) - Austrian-born actor Arnold Schwarzenegger, the leading Republican candidate for California governor, called for a clampdown on illegal immigrants from Mexico on Tuesday as Gov. Gray Davis launched a series of TV ads aimed at keeping his job.
Schwarzenegger, who says it took him 15 years to become a legal U.S. citizen, tackled the politically combustive issue of illegal immigration in response to attacks by Democratic recall rival Cruz Bustamante.
Bustamante had accused the "Terminator" star of being anti-immigrant for supporting Proposition 187, the voter-approved measure that sought to deny public services to people in the country illegally.
"What he doesn't understand is that people like myself waited 15 years to get citizenship," Schwarzenegger, who came to the United States from Austria in the 1960s, said. "There are people who have been waiting 20 years. I find it unfair to all of a sudden push the whole thing with undocumented immigrants and say they should immediately get citizenship."
The film star told the John and Ken show on Los Angeles radio station KFI-AM 640 in a telephone interview that he wanted stricter controls and beefed-up patrols on the U.S. border with Mexico. He said he was also against legislation, currently being debated in Sacramento, that would give California drivers licenses to illegal immigrants -- a bill that Davis has said he would sign and Bustamante supports.
http://www.freerepublic.com/focus/news/976324/posts?page=92