LOS ANGELES — Republican lawmakers and candidates are increasingly divided over illegal immigration — torn between the need to attract Latino support, especially at the ballot box, and rallying party members who support tougher action.

Arizona’s new measure, which requires that the police check the documents of anyone they stop or detain whom they suspect of being in the country illegally, has forced politicians far and wide to take a stance. But unlike in Washington, where a consensus exists among establishment Republicans, the fault lines in the states — where the issue is even more visceral and immediate — are not predictable.

Conservative Republican governors like Jim Gibbons of Nevada, Robert F. McDonnell of Virginia and Rick Perry of Texas have criticized the Arizona law. But some more moderate Republicans, like Tom Campbell, who is running in the party’s Senate primary in California, have supported it.

The decision on whether to support or oppose the law can have almost immediate political consequences. The latest evidence may be Meg Whitman’s declining fortunes.