El Paso, Texas - As President Joe Biden stepped off Air Force One in El Paso to tour the US border on Sunday, Texas Governor Greg Abbott was on the tarmac waiting.

After greeting the president, the far-right Republican governor handed Biden a sharply worded letter in which he criticized him for pushing "open-border policies" and demanded that he resume construction of the border wall promised, but never completed, by former President Donald Trump.

It was the latest round of political theater for Abbott, who describes the stream of asylum seekers arriving at the southern border as an "invasion" and who in recent months has spent millions of taxpayer dollars busing recently arrived migrants to Democratic-run cities on the East Coast.

It also underscored the fundamental challenges faced by Biden, whose recent efforts to address a historic surge in migration have angered not only Republicans but also some members of his own party and human rights advocates.

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After Biden announced last week that he would expand a Trump policy giving border agents the power to quickly turn back asylum seekers, he was slammed in a joint statement by several Democratic senators for "stranding migrants fleeing persecution and torture in countries unable to protect them."

While migrants from Mexico, Central America, and elsewhere have been swiftly deported under Title 42, a rule invoked by Trump that allows the government to keep out foreigners during a public health emergency, people from Cuba, Nicaragua, and Venezuela – countries variously affected by US policy – were until recently allowed to enter the US, given temporary work permits and granted asylum hearings.

Here in El Paso, shelters have been overwhelmed, and migrants have resorted to sleeping on the streets. Last month, as temperatures dipped below freezing, Democratic Mayor Oscar Leeser declared a state of emergency.

Days before his arrival here, Biden announced new policies that he vowed would "substantially reduce" the number of people attempting to cross the border in order to relieve pressure on cities like this one.

Under new guidelines announced Thursday, Cubans, Nicaraguans, and Haitians who enter the country illegally will be immediately deported to Mexico – without their asylum claims being heard.

It is an expansion of a Biden policy enacted late last year aimed at Venezuelans, who at that time made up the majority of asylum seekers crossing the border.

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The Biden administration says that policy reduced the number of Venezuelans who crossed the southwestern border without authorization from 1,100 a day on average to around 100 a day.

At the same time, Biden announced a new pathway to legal entry for people from the four countries, saying that as many as 30,000 of them would be allowed into the US each month if they applied via an online application from their home country, found a US-based sponsor, and passed a rigorous background check, among other restrictive conditions.

This policy strands tens of thousands of people who have already left their countries and begun the dangerous passage toward the US. Many of them are stuck in cities like Juarez, across the border from El Paso. Others sneaked into the United States and have avoided immigration authorities.

Biden's tour of the border did not take him through the stretch of downtown El Paso where most of the migrants have been staying. He did stop to walk along an 18-foot-high section of mesh border fence, through which the homes of Juarez were visible.

The one thing that everybody he encountered seemed to agree on was that more resources were needed.

That's what he learned from meeting with border agents, and what humanitarian aid workers told him.

"If I could wave the wand, what should I do?" Biden asked an employee at the El Paso County Migrant Services Center, which offers food and clothing to migrants who have been released by the Border Patrol. The answer was more funding.

Biden left El Paso on Sunday evening and headed to Mexico City for a two-day summit with Mexican President Andrés Manuel López Obrador and Canadian Prime Minister Justin Trudeau.