The president's approval stands at a low of 35%, according to the survey by polling firm Buendía & Laredo.
Oil companies will be offered a bigger share of profits and more flexibility in contracts.
Energy Minister Pedro Joaquín Coldwell said government will change rules that scared off potential bidders earlier this month, when it was able to auction only two of 14 blocks in a pivotal oil and gas tender.
Only five private equity deals worth a total of US$2 billion have been announced since the energy reform was approved.