Of the country's five million people, about one million of the poorest could receive up to 30,000 dinars ($22,990) a year each if the initial plan was endorsed, according to government estimates debated at LBPC meetings.
Libyans would forfeit their right to medical services and other traditional public services in return for a share of oil revenues.
The vote to postpone Gaddafi's plan will block further discussions on the distribution of oil money for several months at least.
Various factions in the LBPC will now have time to reach a consensus that commentators say will curb the leader's eagerness to plug the wealth gap between the poor majority of the country and the rich, who many Libyans say monopolise power and money.
LBPCs are Libya's most senior executive and legislative bodies, which vote on laws and government policy. In practice, however, Gaddafi formulates the key policies.
Libyan dissidents wrote in comments posted on the internet that, even if the voters approved the scheme, Gaddafi's plan would not work because government corruption would always prevent a fair distribution of the country's oil wealth.
"None of this will ever happen," one Libyan in Sirte told Al Jazeera. "This is a lie."