From the hardened slums of this city to some of Venezuela’s most populous and economically important states, many of President Hugo Chávez’s supporters deserted him in regional elections, showing it is possible to challenge him in areas where he was once thought invincible. The outcome of Sunday’s vote was the second blow dealt to the president in a year, after voters rejected last December his plan to alter the Constitution to give himself more power. Although it was unclear whether the results would slow his Socialist-inspired revolution or check his power, they could complicate his ambitions to amend the Constitution to allow him to run again.