The District would have a thriving network of homeless shelters spread evenly across the city, if not for the not-in-my-backyard naysaying of alarmed neighbors.

That’s the line you hear, anyway. But as the city embarks on a plan to close the troubled D.C. General shelter and replace it with a series of smaller ones, a clear plurality of D.C.’s likely voters say they would welcome a shelter in their neighborhood.

Asked in the Washington City Paper/Kojo Nnamdi Show poll whether they would support a new shelter nearby, 45 percent of respondents indicated that they would. Just 33 percent signalled opposition.

NIMBYism has long plagued the effort to replace or complement the ostensibly temporary family shelter at the former D.C. General Hospital, which closed in 2001, with shelters of a more manageable size. The urgency of the issue grew with the March disappearance of 8-year-old D.C. General resident Relisha Rudd, apparently kidnapped by a shelter janitor, and the spike in family homelessness last winter, expected to increase further this year. In the past, residents and politicians have opposed efforts to establish new shelters in their communities. Ward 4 Councilmember (and Democratic mayoral nominee) Muriel Bowser, for example, took a stand in 2010 against a proposal to convert the former Hebrew Home for the Aged in her ward into another shelter, arguing that the neighborhood had more than its share of shelters already.

But public opinion may be turning. A local advisory neighborhood commission recently voted unanimously to support the conversion of the Hebrew Home into a residential complex with 90 percent of the units set aside for low-income tenants. And this poll shows that only a minority of residents would oppose a new small shelter in their neighborhood as part of a plan to replace D.C. General.

Views on the matter vary greatly by geography, though. The only two wards of the city whose residents expressed majority support for local shelters in the poll were wards 7 and 8. Those are D.C.’s two poorest wards, so perhaps it’s no surprise that residents there feel a greater imperative to help people most in need of assistance. But residents of the two wards east of the Anacostia River have also complained that they have an excess of subsidized housing as it is, and that the rest of the city should shoulder more of the burden of housing the poor.

Wards 4 and 5 were the only two that registered more opposition to local shelters than support, with Ward 2 showing an even split (though the margin of error is higher in these ward-by-ward breakdowns). Ward 6 had the lowest opposition to shelters, just 28 percent, but also the highest number of undecided respondents.

Men (49 percent) were more likely than women (41 percent) to support local shelters, and Democrats (46 percent) were more likely than Republicans (34 percent) and independents (41 percent) to say so. Black and white voters had similar views on the issue, and middle-aged adults were more likely than young adults and seniors to back nearby shelters.

But one of the best indicators of shelter support was a person’s views on marijuana: The majority of those backing a pot-legalization ballot initiative would also support a local shelter, while the plurality of respondents against the initiative didn’t want a shelter in their neighborhood either.

Photo by Darrow Montgomery