"Even if they say they will close the borders, they will never be able to shut them," said Sanchez, who arrived Wednesday to claim asylum.
Sanchez, 37, said he and his family had travelled for weeks from their native Guatemala, and heard about changes at the border on Tuesday, the day the measure was signed.
"I thought about it and I got discouraged. But I said to myself 'No, in the name of God we are going to get there.' And here we are, more inside than outside."
Biden's executive order is intended to bar migrants who enter the US illegally from claiming asylum when averages surge past 2,500 in a day -- a threshold that is presently always passed.
However, it appeared to be business as usual in Jacumba Hot Springs, California when AFP visited on Wednesday and Thursday.
"Nothing has changed," said a Border Patrol officer on condition of anonymity after counting the dozens of migrants waiting to be taken to processing centers.
US media, citing sources with access to the data said 4,000 migrants were apprehended at the border on Wednesday.
Alex Roman, a 31-year-old Colombian who took the same arduous route as Sanchez and his family, also heard about the decree when he was on the Mexican side.
"I just had to push through. I've invested a lot of money in trying to get here, so why would I turn back without trying?"
Thorny issue
At the foot of the wall that marks the international frontier on this stretch of the border, AFP counted around 80 migrants from India, China, Honduras, Nicaragua, Turkey, the Dominican Republic and Jordan who were waiting for a chance to plead their cases.
Biden's border move is an attempt to neutralize criticism of his management of immigration, an issue with which polls show he is struggling ahead of November's rematch presidential election with Donald Trump.
The number of illegal crossings along the 2,000-mile (3,000-kilometer) border have reached new records during his administration, hitting 10,000 in a single day in December.
The number has dropped in recent months, but the issue is proving thorny for Biden.
Trump routinely rails against immigrants and what he says is a catastrophe at the border, pledging mass deportations and an end to illegal migration.
Biden's order would allow him to "suspend the entry" of migrants when the daily average of encounters exceeds 2,500 for a week.
This figure is lower than the daily average since February 2021, said Adam Isacson, a migration specialist at the Washington Office on Latin America, a human rights NGO, so the measure should take effect immediately.
'Promised Land'
Biden is facing opposition on all sides for his handling of the border.
While his Republican opponents say he is not tough enough, some Democratic Party allies say the new rules are overly restrictive.
They note the similarities with a decree issued by Trump in 2018 when he was president, which was blocked in court by an American Civil Liberties Union lawsuit. The ACLU has pledged to go to court again over Biden's action.
One of the differences is that Biden's order allows for exceptions to the blanket rule, including for unaccompanied minors.
On Wednesday, two teenagers from Jordan crossed into the United States alone.
"Their parents stayed in Mexico," said a volunteer who assisted the young people with food and water while they waited for the border patrol.
"They came together but at the last minute, scared by the decree, the parents decided not to cross and send them instead. Their uncle lives here," said the woman.
In the distance, another group of migrants from Colombia and Peru arrived on foot, exhausted, after crossing through another gap in the imposing border wall.
Many of those AFP spoke to said the decree -- like Trump's border wall -- would not stop them.
"There are people here from many countries here... it is a worldwide issue," said Roman, the 31-year-old from Colombia.
"I think it is something that never ends, because for everyone, the United States is the American dream, our promised land."