Any delay would have consequences not only for the immigrants covered by the program, but also for the businesses who employ them, the letter said.

It was up to Congress to determine whether to pass legislation that would extend those protections that would “allow them to continue contributing to the only nation they have known,” the former secretaries said.

“Not only is there no reason to delay, but establishing this new program in 45 days would be an incredible accomplishment done in record time,” the letter continued.

Aides to the Republican and Democratic leaders of the House and Senate declined to comment.

The meeting with congressional leaders on Wednesday is intended to focus on a deal to raise strict limits on military and domestic spending, but all parties expect DACA to come up.

Mr. Trump, pushed by his more anti-immigration advisers, kept a campaign pledge to rescind DACA, despite privately expressing misgivings to aides about doing so. Democratic congressional leaders, who were criticized by activists before the holiday recess for not getting legislation passed, have said they hope to reach a deal, and Senator Mitch McConnell, Republican of Kentucky and the majority leader, has said if there is bipartisan agreement on such a deal, he will bring it to the Senate floor for a vote.

Publicly, the president has insisted on funding for his promised wall along the southern border with Mexico, as well as other security measures, as part of a deal. Some of Mr. Trump’s advisers say they anticipate him signing off on a deal, regardless of concerns among conservative members of congress and certain West Wing aides. John F. Kelly, the White House chief of staff, is said to favor a deal as well, although he is not expected to attend the meeting on Wednesday.