The City Council on Wednesday overwhelmingly rejected a proposal by councilors Frank Baker and Bill Linehan to add a 2% tax on liquor sales to fund addiction treatment programs.

Council President Michelle Wu joined Baker and Linehan in voting for the tax; the other 10 councilors voted against.

Baker and Linehan both gave impassioned pleas for the $20 million they said the measure would raise to help alcoholics and drug users break their addictions.

They said Boston needs to do something at a time when addiction rates are on the rise and suburbs keep sending their addicts to Boston, taking up what relatively few treatment beds the city has available.

Baker, whose father battled alcoholism, said the money could pay for mandatory 30-day "lockdown" beds, which would help addicts get past the five-day drying out period now more typical in recovery units, which only leaves addicts "sick in the head and sick in the stomach," he said.

And he said Boston and local recovery programs need to "stop coming up with bullshit names for things," such as trying to recast Methadone Mile as Recovery Road.

Linehan said the tax would fall heavily on big-spending tourists, not residents, and that Boston needs to start coming up with revenue sources that do not include increasing property taxes.

Linehan also tallied up the costs of addiction on everything from police and fire departments to schools.

"Think of 'The Night of the Living Dead," Linehan said. "That virus they have in the movie makes them want to bite somebody else. ... This is a progressive disease. ... The gift of sobriety to our city is what this bill would do to us. And next Christmas would be a better Christmas."

But Councilor Ayanna Pressley (at large), whose father was addicted to opioids, said the measure was simply too vague. Pressley said she's not opposed to such a tax but that one thing she's learned in 23 years in government - 8 as an elected official - is that "good intentions and more money do not solve problems," that the city needs specific plans before she would vote for any sort of addiction-related tax increase.

She added, "Boston should not uniquely bear the entire burden for an issue that is affecting the entire state."

Pressley and councilors Annissa Essaibi-George (at large) and Tito Jackson (Roxbury) agreed that it would be unfair to burden local residents and small businesses with a tax to solve a problem that is statewide and national in scope.

"This isn't a battle we can fight alone," Essaibi-George said. "We need other cities and towns, the state, and the federal government, to step up. ... I will not lay that burden on the backs of our small business owners before others step up."

Essaibi-George and Jackson aid Gov. Baker should be ashamed of himself for cutting nearly $2 million from addiction services last week.

Other councilors did not speak before voting.