... Catholic Church, such as the US Conference of Catholic Bishops.
From the Pope's message announcing the upcoming 99th World Day of Migrants and Refugees on January 13, 2013 (link, bolding added):
...Certainly every state has the right to regulate migration and to enact policies dictated by the general requirements of the common good, albeit always in safeguarding respect for the dignity of each...
... UPDATE 3: Not surprisingly, the US Conference of Catholic Bishops has come out in support of the evangelicals' letter.
6/14/12 UPDATE: The National Immigration Forum supports the Table too.
On a related note, one of the groups originally signing on is Focus on the Family, and that's created trouble in paradise.
Immigration Equality executive director Rachel B. Tiven says here:
... countries; see the link. The US Conference of Catholic Bishops are enabling bad parenting: they're encouraging people to put their children in a precarious situation rather than encouraging them to remain in their home countries and reform their systems. The Bishops are in effect encouraging people to try to cross the desert, with some dying along the way (see false compassion).
What the U.S....
... (Washington Diocese), Kevin Appleby (US Conference of Catholic Bishops, Sister Ann Curtis (Sisters of Mercy)
* Leadership Conference on Civil Rights: Wade Henderson, Nancy Zirkin
* American Friends Service Committee: "Ruth" from the Friends Committee on National Legislation
* Esperanza USA: Luis Cortes
* Sheryl Sandberg Facebook
* Howard Buffett: Buffett Philanthropies (Warren Buffett)
National Immigration Forum
US Conference of Catholic Bishops
Hebrew Immigrant Aid Society
American Council on International Personnel
Fragomen, Del Rey, Bernsen and Loewy LLC (Fragomen Del Rey, law firm)
Chris Gafner and Stephen Yale Loehr (attorneys)
 From huffingtonpost.com/2011/08/18/skilled-worker-visa-reform-business-white-house_n_929944.html
by Alex Wagner...
... Border Action Network (link)
* the US Conference of Catholic Bishops' "Justice for Immigrants" campaign (justiceforimmigrants.org/whats-new.html)
* breakingbreadwithfamilies.org / changetakesfaith.org
If anyone can find other questionable groups involved please leave a comment.
3/16/10 UPDATE: From this:
Organized by the Center for Community Change (CCC), the March 21 event will be the largest...
Between October 19 and 26, a group of far-left religious groups  will be conducting a "Media Violence Fast" during which they're encouraging their members to avoid violence in the media; that wouldn't be such a bad goal if all they were doing was avoiding entertainment programs. Of course, they aren't doing just that. Instead, they're using the "hate speech" label to both paper over the fact...
On January 12, 2006, the American Bar Association held a conference called "Fortress America: Comprehensive Immigration Reform" at the National Press Club in Washington DC in support of that "reform" and specifically in opposition to HR4437. The brightest lights in the amnesty firmament showed up, all in support of amnesty. I saw video of the event on CSPAN (IIRC) at the time, and it would be...
U.S. News has uploaded a PowerPoint presentation the White House has regarding their new illegal alien amnesty scheme in this PDF file. Even by the abysmally low standard of other Bush administration plans, this is idiotic. Most of the provisions in there would not appeal to even the most cravenly corrupt Democrat, so this isn't a good bargaining ploy. And, it allows the far-left illegal...
A U.S. coalition of business, labor unions and religious groups launched a campaign on Thursday to defeat a bill backed by Republicans that would turn some 11 million illegal immigrants into felons.
The coalition of 24 organizations, many of which rarely agree on politics or economics, denounced the bill passed by the House of Representatives last month and called on the Senate to...