Committee Chairman Tom LaBonge says many patrons are for it, and there's been little resistance from business owners.
"The restaurant association of California is neutral on this, because there are more people who are against smoking than are for smoking," LaBonge said.
Following the lead of Southland cities like Santa Monica and Beverly Hills, the L.A. ordinance would bar customers from lighting up within a 10-foot radius of all outdoor seating areas at restaurants and food courts.
The ban would also do away with smoking 40 feet from mobile food trucks and refreshment kiosks.
"I think that's fair," Los Angeles resident Angela McCrae said. "It's preserving the health of other people. I mean, it's a nuisance to me, so I'm for it."
"Outside I don't think is a problem. I think it's okay," said L.A resident Angel Cordero. "As long as you're in an area that has enough room for people to breathe freely."
There is an exception for age-restricted venues like bars and nightclubs, which would be exempt.
To avoid a heavier caseload, the current draft hasn't assigned a city agency to enforce the ban. Instead, restaurants would be required to post signs and make sure their patrons weren't in violation.
The committee overseeing the ordinance will take up the issue again in six weeks, with a vote going to city council by the middle of December.