The proposal of shared goals -- "Come Let Us Reason Together Governing Agenda" -- is a call to Obama and to Congress to end the "culture wars."
Spearheaded by the progressive think tank Third Way, it includes religious leaders such as the Rev. Joel C. Hunter and David Gushee, religion scholar Robert P. Jones and the religious group Faith in Public Life.
The agenda calls for agreement on four central issues: reducing abortions by increasing support for pregnant women and new families and adoption; protecting the rights of gays in the workplace, with an exemption for faith-based employers; renouncing torture; and supporting immigration reform.
"We are looking for principles in common: respect for human dignity, the golden rule, pragmatism and optimism are the common threads of the project," said Rachel Laser, director of Third Way's cultural program.
Asking Warren and Robinson to share a role in the inauguration is exactly the kind gesture this country needs, she said.
"Obama is a man of the big tent, letting more people come into the tent of progressive politics, expanding the tent to include someone like Warren and to simultaneously choose someone like the first openly gay bishop," Laser told ABCNews.com.
For Laser, who supports abortion rights and is Jewish, connecting with evangelicals such as the Orlando mega-church pastor Joel Hunter, was daunting but ultimately transforming.
She remembers meeting Hunter, pastor at Northland Church in Orlando, Fla., to show him her project. "Once you foster trust and create an environment that feels safe, it's not as hard as you think," she said.
Hunter, who opposed gay marriage and abortion rights, told Laser, her proposal "touched my heart." He is working on a pastor's manual, with research and Scripture, to help his 12,000-strong parish understand the problems of workplace discrimination for gays, among other issues.
"We believe we are at a watershed moment in the country's history," Hunter said at a press conference announcing the agenda last week.
"The culture wars vilify those who are different from us by treating them as traitors and threats," said Hunter, a one-time president-elect of the Christian Coalition. "We can end the culture wars and both sides can advance without compromising our core basic values. It's a new form of maturity."
As for Warren's invocation, Hunter is hopeful. "I know him, and though I haven't talked to him about it, it'll be a good prayer," he told ABCNews.com.
Like Hunter, theologian Reese is looking for an ecumenical prayer from Warren.
"A prayer that divides the nation is not helpful at this point," said Reese. "The desire is that the largest number of people can say amen and feel they have been included."
"Both sides can get overexcited about this issue, but even most atheists are happy to remain silent," he said.
"If they dropped the prayer, I wouldn't protest," Reese said. "The prayer isn't going to save the country, and not having it isn't going to plunge us into disaster. We have to be reasonable and balanced on this."