Most Americans see illegal immigration as a very serious problem, a new CBS News poll shows – a figure that has held steady over the past four years.

Now, 56 percent of Americans say it is a very serious problem, according to the poll, conducted May 20 – 24. An additional 28 percent called it a somewhat serious problem. Only 14 percent said it was not too serious of a problem or not a problem.

Last month, when Arizona Gov. Jan Brewer signed a controversial immigration bill into law, the percentage of Americans calling immigration a very serious problem increased to 65 percent.

But by comparison, 56 percent also called illegal immigration a very serious problem in December, 2007, while 54 percent said the same in October, 2006.

The new Arizona law gives police the power to question someone they have already stopped, detained or arrested about their legal status in the country, and requires people to produce documents verifying their status if asked. About half of Americans (52 percent) see the new Arizona law as about right, the poll shows. Twenty-eight percent think it goes too far, and 17 percent think it does not go far enough.