Foley had represented the West Palm Beach district for 12 years and was seeking re-election until his sudden resignation last week after the disclosure of lurid online communications with teenage congressional pages.
"This is part of his recovery," David Roth said, declining to identify the clergyman or the church.
Roth also announced for the first time that Foley is gay. He insisted Foley never had sexual contact with a minor.
While Foley's career ended last Friday, the one in jeopardy belongs to House Speaker Dennis Hastert, reported CBS News correspondent Gloria Borger.
Hastert, R-Ill., on Tuesday rejected a call from the conservative Washington Times for him to resign over his handling of the scandal.
Majority Leader John Boehner, in a letter to the newspaper, also rejects the call for Hastert to step down.
"No one in the leadership, including Speaker Hastert, had any knowledge of the warped and sexually explicit instant messages" Foley allegedly sent to a teenage page.
Boehner also says Hastert had assured him months ago that the matter had been taken care of. "It's in his corner, it's his responsibility," Boehner, R-Ohio, said in an interview on WLW Radio in Cincinnati.
On the road Tuesday in Stockton, Calif., President Bush added his voice to the chorus reacting to the allegations.
"I was dismayed and shocked to learn about Cong. Foley's unacceptable behavior," said Mr. Bush, who is in the West on a trip to support the campaigns of GOP candidates. "I was disgusted by the revelations and disappointed that he would violate the trust of the citizens who placed him in office... Families have the right to expect that when they send their children to be a congressional page in Washington, that these children will be safe."
The president also said he supports Hastert's call for a full investigation.
Mr. Bush expressed confidence in the speaker's ability to resolve the matter, calling him a "father, teacher, coach."
"I know that he wants all the facts to come out and he wants to ensure that these children up there on Capitol Hill are protected," the president said. "I'm confident he will provide whatever leadership he can to law enforcement in this investigation."
One senior House Republican tells CBS News that there's a lot of anger at what he describes as "a network of gay staffers and gay members who protect each other and did the Speaker a disservice."
Foley resigned abruptly on Friday and has since checked himself into an alcohol rehabilitation program at an undisclosed location.
To speak to former pages like Blake Yocum, Foley's interest in the young students was practically legendary, reported CBS News correspondent Sharyl Attkisson, but this story has been a surprise.
"I feel my close friends who were pages suspected that Congressman Foley was homosexual. But we never suspected pedophilia out of the congressman," said Yocum.
Foley's attorney, David Roth, said Monday that Foley was "absolutely, positively not a pedophile" and had never had inappropriate sexual contact with a minor.
Foley's departure leaves a trail of questions concerning the e-mails and instant messages he allegedly sent pages over an unknown period of time. Beyond the details of his actions, Republican leaders fear the impact on the Nov. 7 elections, and the possible loss of their House majority.
Hastert and other leaders have laid out a complicated series of events. They say they first became aware of overly friendly e-mails from Foley to one underage male page about a year ago, but had no idea that the congressman had sent other, sexually explicit messages, to additional pages.
The speaker has said that Foley was confronted about his communications with the one page, and told to break off contact with him and all other pages.
Boehner, the second-ranking GOP leader, became the latest member of the party's high command to outline his involvement when he answered questions in his radio interview.
"I believe I talked to the speaker, and he told me it had been taken care of," he said, when asked about the e-mails that were not sexually explicit.
"In my position, it's in his corner, it's his responsibility. The clerk of the House, who runs the page program, the page board, all report to the speaker, and I believed it had been dealt with. Again, I didn't know the context of what even the original message (said)," he added.
Boehner, noting that his daughter was a Senate page several years ago, said of Foley: "If I'd known anything about the context of all this when it occurred, I'd have drug him out of there by his shirt sleeves."
ABC News reported instant messages between Foley and a San Diego teenager who suggested he was uncomfortable in an exchange discussing dinner plans for when the boy was to come to Washington.
"… and then what happens," Foley messaged at one point.
"I have the feeling that you are fishing here ... I'm not sure what I would be comfortable with ... well see," the teen replied.
Democrats protested that the matter should have been brought to the attention of the page board or the House Ethics Committee.
"Republican leaders admitted to knowing about Mr. Foley's abhorrent behavior for six months to a year and failed to protect the children in their trust," said Minority Leader Nancy Pelosi, D-Calif. "Republican leaders must be investigated by the Ethics Committee and immediately questioned under oath."
The FBI has begun an inquiry into Foley's computer contact with pages, and Hastert wrote a letter to Florida Gov. Jeb Bush asking for an investigation into whether state laws were broken.
The St. Petersburg Times and The Miami Herald, which had been given copies of the e-mail with the Louisiana boy last year, defended their decisions not to run stories.
"Given the potentially devastating impact that a false suggestion of pedophilia could have on anyone, not to mention a congressman known to be gay, and lacking any corroborating information, we chose not to do a story," said Tom Fiedler, executive editor of the Herald.