A United States Border Patrol agent keeps watch from a secondary wall separating Mexico and the United States in Imperial Beach, California in this November 5, 2010 file photo. (Eric Thayer/Reuters)

REPUBLICANS HOWLED in November when President Obama used his executive powers to shield millions of illegal immigrants from deportation, accusing him of usurping Congress’s powers. Yet as the GOP lays out its agenda for the new Congress, Republicans have had nothing useful to say about their own plans for addressing the problem of the 11 million immigrants who lack documentation.

Like the Republicans, we worry that Mr. Obama’s executive order attempts to accomplish what should be done through legislation. Yet we also recognize that he acted to fill a policy vacuum created largely by Republican intransigence and inertia. If the Republicans want to lend weight to Mr. Obama’s justification for his actions, they are doing a fine job.

In announcing his executive action, Mr. Obama threw down a gauntlet to Republican leaders, daring them to seize the initiative, enact legislation to address the problem of illegal immigration and negate his unilateral move. Rather than take the challenge, Republicans now appear intent on confirming their image as the party of no solution to the immigration dilemma.

Perhaps in the new Congress the GOP will enact a bill allowing holders of foreign passports to remain in this country more easily after graduating with advanced degrees from U.S. universities. Such a measure would make sense as a means to limit the brain drain of U.S.-educated scientists, engineers, mathematicians and high-tech workers.

Perhaps Republicans will vote for further manpower and technology to tighten security on the Southwestern border, although it is already more tightly controlled than at any time in decades.

But no one can claim to have dealt with America’s broken immigration system without reckoning with the reality of 11 million unauthorized people. The country needs their labor but refuses to allow them and their families any way out of the legal shadows.

Rather than fashioning a solution, Republicans remain in a protracted temper tantrum over Mr. Obama’s unilateralism. In an attempt to punish the White House, they funded the Department of Homeland Security only through February. DHS controls most government agencies dealing with immigration.

Threatening the department’s funding — and by extension, its 240,000 employees, a fifth of whom are Hispanic Americans — is a terrible idea, politically and substantively. As Homeland Security Secretary Jeh Johnson warned, it subverts long-term planning and could derail the hiring of new agents for the Secret Service, which also comes under the department’s purview.

At the same time, it is unlikely to derail Mr. Obama’s program to give temporary protection from deportation to 4 million or so immigrants, funding for which would be provided mainly by fees paid by the immigrants themselves.

GOP congressional leaders, seeking to rebrand their party as one dedicated to accomplishment, have pledged quick action on energy and health care. Yet no one will fail to notice the party’s continued inaction on this critical problem.