CARACAS, Venezuela—Right after Hugo Chávez swept to the presidency in 1998, lawmaker Henry Ramos Allup sat alone in his routed party’s abandoned headquarters.

The rise of the populist leader nearly obliterated Mr. Ramos’s Democratic Action party. No one had paid the light or water bills, and the bulk of his colleagues had deserted him to join the new firebrand president. “Even the rats had left to join Chávez,” Mr. Ramos recalled. “All we had left were the cockroaches.”

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