SACRAMENTO — The Rev. Samuel Rodriguez had been summoned to the White House for an urgent meeting, and with so much at stake, he decided that he needed a blessing.

He looked out at the Latino families jammed into his evangelical church in Sacramento on a recent Sunday and called on Stephania Herrera, a youth pastor who had come to the United States illegally when she was 10 years old. Ms. Herrera has been allowed to remain in the country under a program known as DACA. But with that program coming to an end, Mr. Rodriguez was to meet with White House aides to discuss how to save people like Ms. Herrera, known as Dreamers, from deportation.

“Father,” Ms. Herrera said in Spanish, closing her eyes, gripping the microphone with her left hand and holding her pastor’s hand high with her right, “You have placed him in this place, at this time, in this hour, with a great purpose, and we unite as one believing in your purpose. We ask that you send him covered in favor — send him in power — send him with authority.”

The meeting in Washington would not end in success. At President Trump’s urging, Mr. Rodriguez agreed to support a deal that would allow the Dreamers to stay, in exchange for Congress authorizing funding for a border wall, cutting legal immigration and limiting family reunification. But the proposal went nowhere in Congress. And more than a month later, the long-term prospects for roughly 700,000 Dreamers remain in limbo.