"He really ought not be a sacrificial lamb," former Secretary of State James Baker III told CBS News on Friday.
President Bush called Hastert late Thursday to reassure him amid allegations that the House speaker did not do enough to protect the teenage House pages from former Rep. Mark Foley's advances.
Senate Majority Leader Bill Frist, R-Tenn., issued a statement supporting Hastert Thursday night. And Mr. Bush's father, the former President Bush, spoke up for him during an ABC News interview.
The boost comes after a week of wavering support from House Republicans in the wake of revelations that Foley, R-Fla., had been sending inappropriate e-mails to teenage pages for years.
Also Friday, the Los Angeles Times editorial board called for Hastert to resign because his "leadership of the House was already bad enough before the Mark Foley scandal."
Hastert had blamed Democrats for the election-season revelations, but on Thursday abruptly changed course and took responsibility for the matter.
Hastert vowed not to resign over his office's handling of the scandal — "I haven't done anything wrong," he said — but it has cost Republicans in public opinion polls.
"I'm deeply sorry this has happened and the bottom line is we're taking responsibility," Hastert said at a news conference outside his district office in Batavia, Ill.
That seemed to quiet rumblings about Hastert's resignation as the week drew to a close and House and Justice Department officials launched separate investigations.
Baker told Early Show co-anchor Harry Smith that Hastert deserves credit for urging a probe of a sex scandal in the shadow of the midterm elections. And he offered a pragmatic reason for the party to stand by him.
"If they throw Denny Hastert off the sled to slow down the wolves, it won't be long before you'll be crying, 'Hey, you've got to throw somebody else over because they knew about it too,"' Baker said.
Privately, though, CBS News correspondent Gloria Borger reports Republicans say Hastert's mea culpa was the least he could do, but they're far from sure it will be enough.
On the record, they're trying to be upbeat.
"Hopefully, he's cleared the air so members and challengers can have this off the front pages of the paper," said Rep. Ray Lahood, R-Ill.
But other House Republicans remain panicked by the Foley scandal and wonder if the only way to recover is to jettison Hastert.
The speaker told conservative activist Paul Weyrich, that he'll do what's necessary.
"If he thought by resigning that he would help Republicans keep their majority, he would do so," Weyrich said.
Here's why it could come to that, reports Borger: With elections a month away, some internal Republican polls and House races across the country show what one strategist calls "a significant receding of our numbers."
An Associated Press poll shows that about half of all likely voters consider the scandal in Congress