Support for the amendment dips when voters are told that the new measures carry a cost of $46 billion. When that information is shared, 53 percent say they support the bill, with just 43 percent of Democrats and half of independents backing the proposal. Still, three-quarters of Republicans say they back the measure, even when told the cost.

President Obama has looked to regain momentum on the immigration reform effort, sitting for four interviews with Spanish-language television stations earlier this week. 

In the interviews, the president conceded that, despite pressure from the Senate and White House, he doesn’t expect the House to pass an immigration reform bill before the August recess. He had demanded earlier this year that Congress finish work “by the end of summer.”

“I don’t think that we’re gonna see it before the August recess,” Obama told Telemundo. “That was originally my hope and my goal, and if, in fact, the House recognized the smart thing, the right thing to do was to go ahead and send the Senate bill to the floor for a vote, I think it would pass tomorrow.”

But the president said he was hopeful a compromise deal could “happen in the fall.”

“We need to just go ahead and get this done,” Obama said. “I know it’s tough. I know the Republican House members are wrestling with it. Many of their constituencies are suspicious of what immigration might mean for their political futures in some cases. But, you know, one of the things that I know from traveling all around the world is that part of what makes America special is that we attract talent from everywhere, and we wanna make sure that continues to be the case.”

The Post/ABC poll surveyed 1,004 adults and carried a margin of error of plus or minus 3.5 percentage points.