Immigration was a losing issue in the 2014 election, with Republicans who announced their opposition to President Obama’s legalization plans earning victories across the country and voters in Oregon easily defeating a referendum that would have granted driver’s licenses to illegal immigrants.

Republicans said the results should serve as a warning to President Obama, who has said he plans to take unilateral action to grant legal status to illegal immigrants some time this year.

Hispanic leaders had been counting on Oregon voters to embrace driver’s licenses for illegal immigrants, arguing it would be a signal that states were stepping in to act on immigration reform where the federal government wouldn’t.

But when put to voters, the referendum was losing by more than a two-to-one margin as of early Wednesday morning.

In congressional races, Republicans who promised a crackdown on immigration were unseating Democrats who voted for legalization in North Carolina, Arkansas and Colorado, with a December Senate run-off in Louisiana offering yet another test.

Sen. Jeff Sessions, an Alabama Republican who has led opposition to Mr. Obama’s immigration plans, said the results show voters gave a clear mandate to the president.

“Republicans campaigned for the House and Senate against the Obama-Senate immigration bill and on the pledge to block President Obama’s unlawful executive amnesty,” Mr. Sessins said. “The immediate emergency facing our new majority will be fighting the president’s disastrous planned actions, and we will have not only a constitutional mandate but also a popular mandate to do so.”

Democrats and immigrant-rights advocates, though, said Mr. Obama must not be cowed by the election results.

“The fact is that the president has the moral responsibility and the full authority under existing law to expand relief and end the policies he himself has described as inhumane. Good policy should not be subject to bad politics,” said Pablo Alvarado, executive director of the National Day Laborer Organizing Network.

Mr. Obama had planned to take his unilateral action at the end of the summer but put that on hold, with the White House saying it didn’t want to act before the election – which would have given voters a chance to register their disapproval.

In the wake of the election, some liberal analysts said Mr. Obama may have actually squandered a chance to help Democratic candidates win support among Hispanic voters in North Carolina and Colorado by refusing to act, and they said he cannot break his promise yet again.

For their part, Republicans – who will have control of both chambers of Congress – will have to decide how to tackle the issue next year.

Some leaders suggested late Tuesday that they will try to pass legislation solving all parts of the issue, but rank-and-file GOP members warned against that, saying more work must be done first on border security.