Mayor Ed Lee has let it be known that if he has his way, Supervisor David Campos’ proposal to build a safe injection site where intravenous drug users can legally shoot up is not going to happen. No way, no how.

“We have a vigorous disagreement over allowing people to inject heroin and meth, to literally destroy their bodies and their minds, in a city-funded shelter, as some have proposed,” Lee told the Board of Supervisors.

But Lee may actually be in the minority on this one. A new poll by David Binder Research shows that 72 percent of likely voters in state Senate District 11 — San Francisco and the very northern Peninsula — support supervised injection sites.

The poll was commissioned by Drug Policy Action, the political branch of Drug Policy Alliance, a national group that advocates the reform of drug laws. It was conducted from March 1 to 6 and surveyed 400 regular voters. The margin of error is plus or minus 4.9 percent.

The respondents were asked whether they support “providing supervised injection services, which are programs that reduce public drug use and discarded syringes by allowing medically supervised drug use indoors and away from public streets.”

Thirty-four percent said they strongly support it, 38 percent said they somewhat support it, 12 percent said they somewhat oppose it and another 12 percent said they strongly oppose it. Guess Lee’s in that second 12 percent. (Four percent basically said, “Huh?”)

When told more about the pros and cons of safe injection sites — including that opponents believe tax dollars should not pay for “a safe haven for substance abuse” — 65 percent still supported it.

Laura Thomas, deputy state director of the California Drug Policy Alliance, said San Franciscans are very concerned about homelessness, public drug use and discarded needles.

“People are reaching for new solutions and are reaching for good ideas,” she said. “Even if people don’t know much about supervised injection services, the idea makes sense to them.”

The idea of a “wet house” where homeless alcoholics can imbibe inside — proposed by Campos and tepidly supported by Lee — garnered support from 64 percent of the poll respondents.

Respondents to the Drug Policy Action poll were also asked how important it is that the city address a variety of subjects related to homelessness. Mental health treatment, finding housing for the homeless, dealing with feces and urine on the street and dealing with discarded syringes were the top concerns.

Hear that, Mayor Lee?

Family man: At age 45, Assemblyman David Chiu is all grown up.

He and his wife, Candace Chen, had their first baby on Leap Day, Feb. 29, and named the 8-pound, 6-ounce bruiser Lucas Young-San Summer Chiu. (The Chinese middle name roughly translates to “spreading goodness” and was selected by the tyke’s grandparents.)

Also, Chiu and Chen have purchased their first home. It’s a two-bedroom condo in the Candlestick Point area of the Bayview, and they bought it for $770,000. It’s telling that in this exorbitant city, a state politician and a lawyer are priced out to the far corners of San Francisco.

And completing the all-grown-up trifecta? Chiu is getting around in an — wait for it — automobile. The avowed bicyclist and former city supervisor used to commute on two wheels from his Clay Street apartment to City Hall, but the Bayview digs, baby and Sacramento job call for a car. He hasn’t purchased one, but is borrowing the vehicle from his in-laws.

We caught up with Chiu as he was about to give Lucas his first bath. “It’s been everything it’s been chalked up to be and more — amazing, exhausting, exhilarating, bewildering,” he said. He was describing having a baby, not politics.

The hardest part so far? Finding good child care.

“Certainly as we are searching for good child care options, it’s making me think every day about the right policy options for thousands of families in San Francisco and millions of families in our state,” he said.

Spoken like a true politician.

Familiar faces: Reading the “War and Peace”-length list of candidates running for the Democratic County Central Committee in June is like entering a time machine.

Not only is Tom Hsieh Jr. running to keep his seat, but his dad, Tom Hsieh Sr. is running, too. The elder Hsieh, 84, was the city’s third Chinese American supervisor, appointed in 1986 and re-elected twice.

Retired Assemblyman Tom Ammiano is running, as are former Supervisors Sophie Maxwell, Bevan Dufty and Angela Alioto.

“It’s such a flashback for me!” Alioto said.

But the biggest name of all to enter the race is John Burton, 83, who is the chairman of the California Democratic Party and former powerhouse in the California Legislature.

Asked why he’s running — a decision that caught City Hall insiders by surprise — the always gruff Burton grumbled, “Why not? People are surprised at a lot of stuff I do.”

His term as state party chair ends in about a year, and Burton said he wants to stay active in the Democratic party.

“My life’s good and all that stuff — I’ve got no complaints,” he said. “But I see all these poor people on the streets, and it’s just not good.”

Behind the scenes, moderates and progressives are vying to control the DCCC so they can hand out endorsements in the crowded November campaigns for supervisor. That means nine current supervisors, a bunch of November hopefuls and plenty of blasts from the past are all running.

By the way, we asked Burton what he thinks of Donald Trump’s candidacy for president.

“He fooled them all, didn’t he? He was supposed to be dead before the first primary,” Burton said. “It just shows that people are not happy with the status quo. If you’re happy with it, you ought to have your head examined.”

Heather Knight is a San Francisco Chronicle staff writer who covers City Hall politics. Email: hknight@sfchronicle.com Twitter: @hknightsf