House Majority Leader Kevin McCarthy indicated Thursday that Republicans won't set up a vote to help immigrants brought to the U.S. illegally as children without language that significantly boosts border security.

"The one thing I would hate to happen here is that we only do the job halfway, and then we have this problem come back to us," McCarthy, R-Calif,., said on the House floor when asked about the chances of bringing up a "Dream Act" bill soon.

"So the president has asked us about border security as well, and I believe we can find a solution here together," he added.

McCarthy didn't specify what border security measures might be part of a bill helping younger illegal immigrants who benefited from President Obama's Deferred Action for Childhood Arrivals program, or DACA.

Democrats have been hoping that that language might be added that calls on the Department of Homeland Security to develop a border security plan, something key Republicans supported a few years ago.

However, Republicans appear ready to go further than that. Next week, the House Homeland Security Committee is expected to mark up a bill providing $10 billion for the construction of a wall between the U.S. and Mexico. It's not clear if that bill might be something Republicans try to move along with a Dream Act bill.

McCarthy was questioned on the floor by House Minority Whip Steny Hoyer, D-Md., who noted that Republicans have no plans next week to call up a Dream Act bill.

Democrats have been pushing for a Dream Act bill since President Trump said he would rescind DACA in March, and called on Congress to legislate protection for those who now use DACA to stay in the U.S. and work.

McCarthy said generally he agrees with Trump's decision to send the issue to Congress, as opposed to living with Obama's program that was not approved by Congress.

"I agree with the president's position," McCarthy said. "Courts have shown that the past was unconstitutional, and that just means the House has to do their job, and the Senate."

"The president has challenged this Congress to find a solution, and I believe we can," he said.