CARACAS, Venezuela—Many among Venezuela’s opposition and its U.S. backers figured President Nicolás Maduro’s regime would crumble quickly after Washington threw its support behind a plan designed to sap his military support and spur his exit. It hasn’t happened that way.

Three weeks after the head of the country’s national assembly, Juan Guaidó, declared himself interim president, Mr. Maduro remains firmly in control, prompting some to call that plan into question.

“The...