“It would be more of a psychological victory, a way to reshape the image of Los Angeles,” said Mr. Elkind, who researches and writes on environmental law at the University of California, Berkeley and the University of California, Los Angeles law schools.

The connection’s absence is, in many ways, what you would expect from an airport that has had few major improvements since the current terminals opened in 1961. Last year, a modernization of the Tom Bradley International Terminal was completed, part of $4.76 billion in improvements that have been planned for the airport.

Connecting the rail lines with Los Angeles International is part of that expansive renovation, which could also include construction of an intermodal transit center — a connection point for trains, buses and shuttles — and a rental car center east of the airport.

The current setup is haphazard and halfhearted. Neither the airport nor the county tracks how many people use the rail-bus connection to reach the airport. On Saturday evening, the shuttle buses were overwhelmingly filled with airport employees, perhaps explaining why one of the two luggage racks on most buses has been removed. On Sundays and holidays, only two buses are available to run the loop, sometimes causing 15- to 20-minute waits, said Whitni Lampkin, who commutes to her job at the airport on the Green Line.

There is broad agreement that these types of infrastructure improvements are needed, and because of the 2008 passage of a half-cent county sales tax increase, the money is available. It is expected to raise $40 billion over 30 years for transportation projects.

But just how the connection is made is where the politics lie.

There are two options drawing the most consideration. One is an underground rail line that would offer more direct access to the airport, at a cost of about $2 billion more, but it would do little to ease airport congestion. The Los Angeles County Metropolitan Transportation Authority, or Metro, board has placed the proposal on the back burner.

The other option, backed by Mayor Garcetti, is centered on what Mr. Bonin, the councilman, describes as building a new front door to the airport, about a mile and a half away. Ideally, it would be not only a transit hub, but also a place where cars could be parked and luggage checked before passengers took an automated people mover that circulated through the nine terminals.