WASHINGTON -- Republican vice presidential candidate Sarah Palin's attack on Democratic White House hopeful Barack Obama as someone who would "pal around with terrorists" has sparked rage and support as both campaigns sharpen their knives in the final push for the presidency.

The issue dominated the Sunday morning talk shows just a month before the election and as Obama's camp has angrily derided McCain for saying it wanted to "turn the page" away from the economic crisis.

On Saturday, McCain's running mate Palin, the governor of Alaska, told supporters in Englewood, Colorado -- and again later in the day before a crowd of 10,000 in Carson, California -- that Obama "is someone who sees America as imperfect enough to pal around with terrorists who would target their own country."

The comment referred to William Ayers, a founding member of the radical 1960s group the Weathermen that committed bombings on the Pentagon and the Capitol, and who supported Obama's first run for public office in 1995.

The Obama campaign blasted the remark as "desperate and false."

But independent Senator Joseph Lieberman, who ran as Al Gore's Democratic vice presidential running mate in 2000 and is now a close ally of McCain, told Fox News Sunday that "it is fair game" to link Obama with Ayers.

"If the shoe was on the other foot and John McCain had one of his earliest campaign events at the home of somebody who had formed a right wing group that had bombed buildings... you bet the Obama campaign would have been raising that question," Lieberman said.

Democratic Senator Claire McCaskill of Missouri fired back: "Really, how ridiculous. American people deserve so much better. Do they really think America is going to think that Barack Obama is palling around with terrorists?"

Senator Sherrod Brown of the battleground state Ohio said the attack was a warning shot that threatens to bring the race down into the mud.

"You've seen a 26-year Senate veteran morph into a desperate angry... candidate in the last few weeks, especially the last few days and it kind of makes me sad... that John McCain and Sarah Palin are resorting to these tactics."

Palin's sharp jab is in step with recent Republican campaign statements that the McCain camp plans to launch a fierce assault on Obama with the presidential election only 30 days away, with top McCain adviser Greg Strimple promising a "very aggressive last 30 days."

Minnesota Governor Tim Pawlenty said the issue was a crucial test of Obama's character and judgment as Ayers hosted a political event at his home when Obama was starting his political career.

"I think when people realize this is about, you know, ten years ago, 14 years ago, it goes to the issue of what kind of judgment would allow an unrepentant domestic terrorist to host a political event for you in his home," Pawlenty said on ABC's "This Week."

Democratic Congressman Rahm Emanuel of Illinois warned there was plenty of ammunition to launch against McCain if the race soured further.

"If we are going to go down this road, you know, Barack Obama at eight years old somehow responsible for Bill Ayers. At 58, John McCain was associating with Charles Keating," who went to prison for his role in a massive savings and loan scandal in the 1980s.