The White House’s chief liaison to Capitol Hill says President Trump is anxious to get a deal on immigration but it’s really up to Democrats as to whether they can rein in their base and get something done.

Mr. Trump went beyond what many were expecting in laying out a plan that provides a pathway to citizenship for some 1.8 million illegal immigrants in the U.S., Marc Short, White House director of legislative affairs, said on “Fox News Sunday.”

“So far, Democrats have continued to cry that they don’t want to solve the problem,” Mr. Short said.

“We’re anxious to solve the problem. The question is, do Democrats, will [Senate Minority Leader] Chuck Schumer and [House Minority Leader ] Nancy Pelosi show the same leadership and protect their constituency from their radical left-wing base? Or they could continue to play politics with this issue,” he said.

The president’s plan has gotten praise from some Republicans, but it’s also been met with criticism from both immigration hard-liners who say there are too many protections for illegal immigrants, as well as from Democrats who say some of the new restrictions go too far.

“We’re anxious to get a deal. We’ve been trying to get a deal. I think that question really belongs to the Democrats in Congress,” Mr. Short said.

The White House official also said conservatives should support the plan, noting that immigration hawks like Sens. Tom Cotton and David Perdue have had positive comments about it.

“I think conservatives recognize the benefit to really securing our border and helping to fix these long-term problems,” Mr. Short said. “So yes, I think we’re going to get widespread support on our side.”

Last year, Mr. Trump announced a March 5 phase-out of the Deferred Action for Childhood Arrivals (DACA) program, which protects certain illegal immigrants brought to the country as children from deportation, and said Congress needed to come up with a solution before then.

Mr. Short said that action in the courts over the program has softened the effect of that deadline somewhat, but that another court could always step in and end the program immediately.