MEXICO CITY -- President Enrique Pena Nieto awoke to a storm of criticism from Mexicans over his decision to meet Wednesday with Republican presidential candidate Donald Trump, who is widely reviled in Mexico for referring to its migrants as rapists and criminals.

Blogger Diego Garcia stood with a handful of protesters at Mexico City's Independence Monument, wearing a green professional wrestler's mask and holding aloft a sign reading "Stop Trump's Insults!"

"This man has called Mexicans a burden on society, so for the president to invite him here in a friendly way, and what's worse, to meet with him in private, well I consider that an insult," said Garcia.

Protesters in Mexico City carry signs saying Glenn Coleman/CBS

Artist Arturo Meade stood nearby with his 2 ½-year old son Mariano and shook his head in disgust.

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"This is an insult and a betrayal," Meade said. "What can this meeting bring us, except surrealism in all its splendor?"

Former President Vicente Fox told local media that Trump was trying to boost his sagging campaign. "He fooled him (Pena Nieto) ... he's using him to try to recover lost votes."

Former first lady Margarita Zavala, wife of ex-president Felipe Calderon and herself a potential presidential candidate, aimed a tweet at Trump, saying: "Even though you may have been invited, we want you to know you're not welcome. We Mexicans have dignity, and we reject your hate speech."

Leading historian Enrique Krauze also addressed a tweet to Trump in English: "Listen ... We Mexicans expect nothing less than an apology for calling us 'criminals and rapists.'"

He compared Pena Nieto's meeting with Trump to British Prime Minister Neville Chamberlain signing of a 1938 peace pact with Germany. "Tyrants are to be confronted, not pacified," Krauze told the Televisa TV network.

Even Pena Nieto has made such such comparisons. Asked about Trump in March, Pena Nieto complained to the Excelsior newspaper about "these strident expressions that seek to propose very simple solutions." He said that sort of language has led to "very fateful scenes in the history of humanity."

"That's the way Mussolini arrived and the way Hitler arrived," Pena Nieto said.

Many Mexicans felt the Republican candidate had left Pena Nieto flat-footed by accepting an invitation the Mexican president had made simply for appearances' sake.

The newspaper El Universal wrote in an editorial that Trump "caught Mexican diplomats off guard" by accepting the invitation, and "got one step ahead of them."

"They wanted to invite Hillary (Clinton), but that meant inviting both of them and nobody thought Trump would accept first," said Mexico City-based security analyst Alejandro Hope. "What's in it for Mexico? Here there's nothing to gain. The upside is all for Trump."

"Poor Mexico .. enough of the Blah Blah Blah" says sign held by protester near U.S. embassy in Mexico City. Mexicans protested the meeting Wed. between Donald Trump and Mexican President Enrique Pena Nieto. Glenn Coleman/CBS

Donald Trump's running mate Mike Pence previewed the Republican nominee's busy Wednesday in an early interview with touching on Trump's immigration policy speech and his hastily arranged Wednesday afternoon with Mexican President Enrique Peña Nieto.

Discussing Trump's proposals to build a wall along the U.S.-Mexico border, Pence told CBS News' Norah O'Donnell: "He hasn't wavered for a minute" on the issue.

And, the vice presidential nominee added, "I expect he'll reinforce that commitment when he meets with the president of Mexico today."

Historically, the golden rule of Mexico's foreign policy has been to avoid being seen as taking sides in U.S. politics; hence the two invitations, even though Mexico favors Hillary Clinton's position on a path to citizenship for migrants.

Pena Nieto acknowledged he had invited both candidates, and said he did it because "I believe in dialogue to promote Mexico's interests and above all to protect Mexicans everywhere."

Mexicans have already made - and beaten to pulp - pinatas of Donald Trump. They created a video game in which players can throw soccer balls, cactus leaves and tequila bottles at a cartoon image of Trump. It remained to be seen how else they could demonstrate their dislike for the man, or how much the meeting could hurt Pena Nieto, whose popularity is already at an all-time low near 20 percent, according to recent polls.

"This is an irrational act by two politicians with image problems," said Mexico City security analyst Raul Benitez. "There is no logic."

Newspaper columnist Jorge Zepeda called the decision to meet with Trump "a monumental error," saying that that Trump is a "loose cannon" who might give his own spin on the private, closed-door meeting.

"The Republican candidate will use this meeting for electoral purposes, to re-position himself with the Latino voters," Zepeda said.

Abraham Garnica, 31, who works as an engineer in Mexico City, was left like most Mexicans, scratching his head while trying to think of a reason why Pena Nieto might have agreed to the meeting.

"They must be afraid he might win, and so they're saying, 'Just in case, we'll shake his hand," Garnica said. "I myself, I wouldn't have invited him."

Peter Schechter, the director of the Atlantic Council's Adrienne Arsht Latin America Center, wrote "It is inexplicable why President Peña Nieto would proactively lend legitimacy to a candidate who has been continuously hostile to the entire country of Mexico."

Newspaper vendor Graciela Valedon, 62, said the meeting at least might be a chance to demonstrate traditional Mexican hospitality.

"Let him meet with him, so that he can't say Mexico didn't show him respect or receive him," said Valdeon. "I wish we were as welcome as they (U.S. citizens) are in Mexico, that we were treated like we treat them."