In Curacao, opposition officials were buoyed by the willingness of the country’s foreign minister to stage aid along a sea corridor long used by Venezuelan migrants to flee the country. But in recent days, plans appeared to be falling apart as politicians in Curacao objected to the use of the aid as a political weapon.

The uncertainty has left some in Venezuela not counting on aid anytime soon.

“They say they are in charge of the government, but the ones who are in charge are the ones who control the bridge,” said Héctor Cárdenas, 52, who crossed the border to buys a month’s worth of cooking oil, vegetables, soap and medicines in Colombia. “The opposition has no real power.”

John R. Bolton, Mr. Trump’s national security adviser, told reporters in Miami before the speech that Venezuelan volunteers would bring in all the donated supplies, with no assist from the American forces that have stockpiled the aid on the Colombian side.

Regardless, the outcome would not be ideal for Mr. Maduro, Mr. Bolton said, because if the Venezuelan military blocked the aid, the world would see Mr. Maduro’s “true colors.”

“We hope that the press will be there to see the Maduro loyalists stopping humanitarian assistance from going to the poor people of Venezuela,” Mr. Bolton said. “People want to know why the Venezuelan people are rising up. That act by Maduro would be proof beyond words.”

In Caracas, the Venezuelan government made its own attempt to turn the propaganda wars on food to its own advantage on Monday.

Communications Minister Jorge Rodríguez said Venezuela would be sending 20,000 boxes of food into Cúcuta, citing Colombia’s history of drug violence and poverty.

“It seems that no one takes care of the Colombian people, especially those on the border,” he said.