The future of the proposed tax, which would raise an estimated $40 billion over the next 30 years, now rests in the hands of the state Legislature.
In order to increase the sales tax, which is already too close to its legal limit in some portions of the county to be raised, the Legislature must approve a bill that would exempt it from the tax cap.
That bill awaits a Senate Appropriations Committee vote, which is expected to occur later this week.
At last Tuesday's meeting, Knabe and Supervisor Mike Antonovich voted against placing the measure on the November general election ballot, resulting in a 2-2-1 vote, with Supervisors Zev Yaroslavsky and Yvonne Burke voting for it and Supervisor Gloria Molina abstaining.
As a result, the motion failed, meaning the tax measure would have gone on a separate ballot on the same day, which county officials estimated could have cost about $10.5 million.
Knabe, though against the tax, said he didn't want to needlessly raise the cost of the election while adding to voter confusion, so he agreed to revive the issue and change his vote.
If the Legislature clears the way for the measure, it would then go before voters, two-thirds of whom must support it in order for the tax to pass.
Meanwhile, in a separate measure proposed by Antonovich and Molina and supported by Knabe, the board voted 3-to-2 to send a letter to the Metropolitan Transportation Authority expressing opposition to the tax.