Opponents say that effort would be unconstitutional, arguing that the power to grant citizenship resides with the federal government, not with the states. Still, the chances of passing many of these measures appear better than at any time since 2006, when many states, frustrated with inaction in Washington, began proposing initiatives to curb illegal immigration.

Republicans gained more than 690 seats in state legislatures nationwide in the November midterms, winning their strongest representation at the state level in more than 80 years.

Few people expect movement on immigration issues when Congress reconvenes next week in a divided Washington. Republicans, who will control the House of Representatives, do not support an overhaul of immigration laws that President Obama has promised to continue to push. State lawmakers say it has fallen to them to act.

“The federal government’s failure to enforce our border has functionally turned every state into a border state,” said Randy Terrill, a Republican representative in Oklahoma who has led the drive for anti-illegal immigration laws there. “This is federalism in action,” he said. “The states are stepping in and filling the void left by the federal government.”

But the proposals have already drawn opposition from some business groups. And they are forcing strategic soul-searching within the Republican Party nationwide, with a rising populist base on one side demanding tough immigration measures, and, on the other side, traditional Republican supporters in business and a fast-growing Latino electorate strongly opposing those measures.