What Rudy Giuliani did last week was stupid. What Scott Walker did ought to disqualify him as a serious presidential contender.

As the world now knows, Giuliani, the former New York mayor, said at a dinner featuring Walker, the Wisconsin governor, that “I do not believe that the president loves America.” According to Politico, Giuliani said President Obama “wasn’t brought up the way you were brought up and I was brought up through love of this country.”

And Walker, just a few seats away, said … nothing. Asked the next morning on CNBC about Giuliani’s words, the presidential aspirant was spineless: “The mayor can speak for himself. I’m not going to comment on what the president thinks or not. He can speak for himself as well. I’ll tell you, I love America, and I think there are plenty of people — Democrat, Republican, independent, everyone in between — who love this country.”

But did he agree with Giuliani? “I’m in New York,” Walker demurred. “I’m used to people saying things that are aggressive out there.”

This is what’s alarming about the Giuliani affair. There will always be people on the fringe who say outrageous things (and Giuliani, once a respected public servant, has sadly joined the nutters as he questioned the president’s patriotism even while claiming he was doing no such thing). But to have a civilized debate, it’s necessary for public officials to disown such beyond-the-pale rhetoric. And Walker failed that fundamental test of leadership.

This past week saw the harvest of a bumper crop of crazy, much of it occasioned by Obama’s efforts to make clear that the United States isn’t at war with Islam, by avoiding the phrase “radical Islam” and by pointing out that terrible things have also been done in the name of Christianity. His language on Islam is essentially the same as George W. Bush’s, but no matter.

Rupert Murdoch’s New York Post put a blindfold over a cover photo of Obama last Thursday with the words “Islamic Terror? I just don’t see it.” Rep. Paul Gosar, R-Arizona, said he found the Iranian regime and Obama “unusually the same” in their disregard for the rule of law. The conservative activist Dinesh D’Souza, tweeting a photo of Obama taking a selfie, added the message: “YOU CAN TAKE THE BOY OUT OF THE GHETTO … Watch this vulgar man show his stuff, while America cowers in embarrassment.”

Over-the-top rhetoric comes from both sides of the political spectrum, and it is always in the background. (Last week, a South Dakota state lawmaker, on his official website, likened Planned Parenthood to the Islamic State terrorists who behead hostages.) The problem here is the venom is being sanctioned, even seconded, by those who would lead the Republican Party.

Sen. Ted Cruz, R-Texas, a presidential aspirant, last week called Obama “an apologist for radical Islamic terrorists.” Another contender, Louisiana Gov. Bobby Jindal, inserted himself into the debate by issuing a statement in support of Giuliani, saying “the gist” of Giuliani’s remarks was true, and “if you are looking for someone to condemn the mayor, look elsewhere.”

Certainly don’t look to Walker, who, in trying to establish himself as the man to lead the country after the 2016 election, is avoiding anything that might resemble leadership.

Earlier this month, in London during the annual Darwin Day observance, he refused to answer a question about evolution. “I’m going to punt on that,” he said at a British think tank. “That’s a question a politician shouldn’t be involved in one way or another, so I’m going to leave that up to you.”

At home in Wisconsin, Walker’s leadership has been conspicuously missing. His tax cuts have left the state with a $283 million deficit that needs to be covered by mid-year and a deficit projected at $2 billion for the two years beginning in July. Bloomberg News reported last week that the state will delay $108 million in debt payments due in May — a move that will ultimately increase the amount Wisconsin has to pay.

And Walker? He was at a dinner in New York with supply-side economists last week, explaining how he can do for the nation what he did for Wisconsin.

That dinner last Wednesday, at New York’s 21 Club, is where Giuliani challenged Obama’s love of country. Even the former mayor preceded his outrageous allegation by saying, “I know this is a horrible thing to say …”

Walker surely knew it was horrible, too, but he refused to say so — and in this failure displayed a cowardice unworthy of a man who would be president.

Dana Milbank is a Washington Post columnist.