LOS ANGELES — The overwhelming majority of Americans think the country’s immigration policies need to be seriously overhauled. And despite protests against Arizona’s stringent new immigration enforcement law, a majority of Americans support it, even though they say it may lead to racial profiling.

These are the findings of the latest New York Times/CBS News poll.

With the signing of the Arizona law on April 23 and reports of renewed efforts in Washington to rethink immigration, there has been an uptick in the number of Americans who describe illegal immigration as a serious problem.

But the poll — conducted April 28 through May 2 with 1,079 adults, and with a margin of sampling error of plus or minus three percentage points — suggests that Americans remain deeply divided about what to do.

The public broadly agrees, across party lines, that the United States could be doing more along its border to keep illegal immigrants out. The view was shared by 78 percent of the respondents.