American Catholic leaders are hoping that President Obama’s meeting with Pope Francis at the Vatican on Thursday will strengthen his resolve to soften U.S. policy on deportations, and that the pontiff’s call for compassion toward migrants will also bolster the prospects for immigration reform, now stalled in Congress.

Church officials have staged several high-profile events to reinforce the pope’s message. On Wednesday, a delegation led by Los Angeles Archbishop José Gomez brought the young daughter of a man facing deportation to meet the pope at the Vatican. Next week, a group of bishops led by Boston’s Cardinal Sean O’Malley will visit the U.S.-Mexican border and celebrate Mass for migrants in Nogales, Mexico.

But although Obama recently signaled that he may be willing to soften the rules on deportation — and the girl’s father was released from federal detention Thursday — there is no indication that the late-hour involvement of even the most senior Catholic officials is likely to move House Republicans to reopen debate on broader immigration reforms.

“What’s happening is extraordinary. Between the pope listening to a 10-year-old girl and Cardinal O’Malley going to the border, this is the best the church has to offer,” said John Carr, a former official of the U.S. Catholic Conference of Bishops now with Georgetown University. “The big question is whether anybody is listening.”

The Obama administration has deported nearly 2 million illegal immigrants, hoping to use that tough policy as a bargaining chip with Congress on broader reforms. Two weeks ago, facing a barrage of protests from pro-immigrant groups and no sign of movement in Congress, the president ordered a review of deportation procedures on humanitarian grounds.

Immediately, however, House Republican leaders warned that such unilateral actions would jeopardize any chance of getting reform back on the table. A spokesman for House Speaker John A. Boehner (R-Ohio) said that any executive action to ease deportations would damage, “perhaps beyond repair, our ability to build the trust necessary to enact real immigration reform.”

Last year, U.S. Catholic officials, whose denomination includes millions of Hispanic immigrants, launched a national campaign for immigration reform, with special appeals to key members of Congress including Boehner, a Roman Catholic. The effort appeared to founder, and some critics said the church had waited too long to have a meaningful impact.

Now, with the clock running out, the Catholic officials are aiming a Hail Mary pass at the issue. On Wednesday, the pope stopped to greet Jersey Vargas, with cameras whirring, while she tearfully asked him to help save her father. On Thursday, the Argentine-born pontiff told Obama that immigration reform is urgently needed, and the president said he responded that “I thought there was an opportunity to make this right and get something passed.”

In the Washington area, Catholic officials expressed excitement and hope at the high-level encounter, saying they hope Francis’s personal appeal will inspire Obama to take action and stop deportations that have separated many Hispanic families.

“Obama has the power to take action, and we hope the Holy Spirit will stay in his heart,” said Father Eugenio Hoyos, who heads the Hispanic Apostolate of the Catholic Archdiocese of Arlington in Virginia. “Just as the church can pardon sinners, our president can give amnesty to people who are suffering. He doesn’t need to wait for Congress anymore.”

Other church officials said the upcoming pilgrimage by O’Malley to the Arizona-Mexico border, billed as an effort to “bring attention to the human consequences of a broken immigration system,” is an unprecedented gesture that they hope members of Congress, especially Boehner, may still heed. O’Malley is considered the pope’s closest church aide in the United States, and he has taken strong conservative stands on issues such as abortion.

“This is extremely important. It is as dramatic as the bishops can get,” Carr said. “Washington is isolated from reality, and the church is reminding them that people’s lives are being torn apart.”