Even U.S. President Barack Obama has directed administration officials to "closely monitor" the civil rights implications of the Arizona law.

Mayor Phil Gordon of Phoenix, capital of Arizona, signaled that he intended to pursue a lawsuit. The Justice Department also could try to intervene legally.

The U.S. Constitution and federal law trump state law. Article I of the Constitution specifically gives U.S. lawmakers authority to establish a "Uniform Rule of Naturalization" and to regulate commerce with other nations.

Legal experts speculate that certain immediate challenges to the law could result in a judge blocking the law from ever taking effect. Other challenges, such as those claiming racial profiling, may require enforcement of the law first to create a test case.

The legislation signed by the Republican governor has also demonstrated the sharp difference between the Republicans and Democrats on the important issue of immigration reform.

"The only thing this law will do is to make it open season for any immigrant, anybody who does not look Anglo, and it will make actually racial profiling legal in Arizona," Democratic communications strategist Maria Cardona told the CBS "The Early Show on Saturday Morning."

Republican strategist Bay Buchanan said on the same show that Arizonan conservatives "had it with the federal government."

"They have refused to do the job and the answer is not amnesty for the 15 to 20 million illegals here," he added.

Meanwhile, a large rally protesting Arizona's new immigration law is planned at the state Capitol in Phoenix Sunday afternoon. Many participants are coming from the neighboring states such as California and Colorado. Similar protests and rallies are expected in California, Florida, New York and other places with a large population of immigrants.

Arizona's controversial immigration law is certain to have sweeping effects that will be felt in all states in the United States.

Former U.S. Congressman Tom Tancredo told 7NEWS he would like to see a similar law in Colorado through a ballot initiative that he would be happy to run.