(AP) -- Any Republican presidential candidate too scared of the GOP political base to condemn Donald Trump shouldn't be president, the White House said Tuesday, lambasting the GOP front-runner's proposal to bar Muslims from entering the U.S.

Calling it "disqualifying," White House spokesman Josh Earnest deemed Trump's plan "offensive and toxic" and warned it would harm U.S. national security. He called on the rest of the Republican candidates to declare they will not support Trump if he wins the GOP nomination.

"If they are so cowed by Mr. Trump and his supporters that they're not willing to stand by the values enshrined in the Constitution, then they have no business serving as president of the United States themselves," Earnest said.

Trump's proposal has been condemned by many Republican candidates but cheered by many Trump supporters. Democrats see Trump's rhetoric about Muslims as potentially damaging to the Republican Party's brand as a whole and have tried to keep the focus on whether the other Republicans will disavow their party's leading candidate.

Yet the White House risked stepping on that message with an offhand comment mocking Trump's appearance. Speaking to reporters Tuesday, Earnest said Trump's campaign has "had a dustbin of history-like quality to it, from the vacuous sloganeering to the outright lies to even the fake hair."

Trump himself has been criticized for commenting on the looks of his opponents, including Carly Fiorina and Rand Paul. Asked why he would bring up Trump's appearance, Earnest said Trump has "a rather outrageous appearance" that illustrates "why it would be easy for people to dismiss the Trump campaign as not particularly serious."

"That's a hallmark of his campaign and his identity," Earnest said.

The blond-coiffed Trump has repeatedly insisted his hair is real. Asked how he was certain it was fake, Earnest replied, "I guess I'm happy to be fact-checked."