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A Gallup poll at the end of April found that 27% of Americans view immigration as the most important issue facing the country, topping the economy and inflation.
A separate poll conducted in March by the Associated Press and NORC Center for Public Affairs Research found that two-thirds of Americans now disapprove of Mr Biden's handling of the border, including about 40% of Democrat voters.
The White House, however, has been largely quiet on the recent drop in migrant arrivals and detentions.
A White House statement in late April said only that Mr Biden and Mr López Obrador had discussed "how to effectively manage" hemispheric migration, adding that both leaders had directed their national security teams to "immediately implement concrete measures to significantly rescue irregular border crossings."
The BBC has reached out to the White House for comment.
Some experts have suggested that the silence is reflective of a White House that is well aware that numbers could begin to climb again - potentially soon.
"I strongly suspect that the administration has finally learned its lesson about declaring victory early. We've seen that in the past, multiple times," said Aaron Reichlin-Melnick, policy director at the American Immigration Council.
"But then after two or three months of lower numbers, they start to creep back up and the administration has to eat crow."
"I also suspect that they are aware that whether or not this is viable remains to be seen, and do not want to draw too much attention to it," he added.
Faced with the possibility of another influx - and the lack of progress passing immigration reforms in Congress - the Biden administration is reportedly mulling a broad executive order that would dramatically limit the number of asylum seekers at the border and essentially shut it down if migrant figures rise above a certain point.
"The question is whether the numbers hold until after the November elections, but if the bubble bursts before November," Mr Isacson said.
"That's when you'd be hearing more rumblings about harsh restrictions...they would probably do that, even if it only meant dropping migration for a few months."