Alexandria Ocasio-Cortez will not take a primary victory for granted.

Just days after her overwhelming victory against one of the most prominent congressmen of the Democratic party, Joe Crowley, the young politician of the Bronx joined Stephen Colbert on "The Late Show" to discuss her victory.

"I want to confess that I did not know your name on Monday,” Colbert told the young candidate of Puerto Rican origin. And like him, most of the country was surprised when Ocasio-Cortez won by a large margin against a tough candidate who was supposed to replace the leader of the party, Nancy Pelosi, after the midterms.

"Most people didn’t,” she replied. "I don’t think polling is always right. People try to identify who’s the most likely person to turn out, and what we did is that we changed who turns out."

Thanks to a campaign based on Bernie Sanders' model, Ocasio-Cortez had a grassroots policy team, with dozens of volunteers going door-to-door carrying her proposal for a new generation joining the Democratic machinery, not without criticizing it from the beginning.

To distinguish herself from the traditional party, the Latino candidate represents the Democratic Socialists, a name that is not easy to swallow for a country accustomed to bipartisanship and with a historical fear of the extreme left.

But Ocasio-Cortez has opted to define her proposal as an urgent need for the country.

"The value for me (of Democratic Socialism) is that, in a modern, moral and wealthy society, no person in America should be too poor to live," she said. "It's pretty simple."

"What that means for me is health care as a human right; that any child, no matter where you were born, should have access to a college or trade school education if they so choose it, and I think that no person should be homeless if we can have public structure and public policy to lead a dignified life in the United States."

But Colbert stressed that, against Donald Trump’s government, these proposals will not be easy to fulfill.

After the president celebrated Crowley's defeat and attributed it to the fact that the congressman is a "Trump hater," the reality of the challenge that Ocasio-Cortez must face is increasingly emerging as a battle like David versus Goliath.

Immediately after her victory, the candidate didn’t hesitate to make clear her position against President Trump, saying that "there were serious grounds to show Trump had violated the Constitution’s Emoluments Clause from day one of his administration," Newsweek reported.

Faced with the presidential verbiage on Twitter, where Trump suggested that Crowley should have been "nicer, and more respectful, to his president," the new Bronx candidate will not be so easily intimidated:

"Well, the president is from Queens and, with all due respect, half of my district is from Queens, but I don’t think he knows how to deal with a girl from the Bronx," she said.