Donald Trump has been condemned for “vile and reprehensible” tweets that trivialize America’s homelessness crisis in an attempt to rebuke the House speaker, Nancy Pelosi, the architect of his impeachment.

On Thursday the president, holed up at his Mar-a-Lago estate in Florida over Christmas, went on the offensive against Pelosi, whose home district includes San Francisco.

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“Nancy Pelosi’s District in California has rapidly become one of the worst anywhere in the U.S. when it come [sic] to the homeless & crime,” Trump tweeted. “It has gotten so bad, so fast – she has lost total control.”

In another post, he wrote: “Crazy Nancy should clean up her filthy dirty District & help the homeless there.”

The diatribe was criticized by advocates for homeless Americans, of whom there are more than half a million on any single night. The president is exploiting the issue for his own political gain, they argued.

Diane Yentel, president and chief executive of the National Low Income Housing Coalition (NLIHC), said: “Trump’s tweets are vile and reprehensible. The only time he utters the word homelessness is to use it as a political cudgel to try to embarrass perceived political enemies.

“Homelessness in California is indeed a crisis, as it is in many other areas of the country – one that demands urgent action at the federal, state and local levels. Federal action to solve the crisis is long overdue, but President Trump has tried, time and time again, to worsen homelessness in our country.”

Trump has proposed drastically shrinking or eliminating federal programs that keep the lowest-income people affordably housed, tripling rents for the lowest-income subsidized residents, and raising rents for all subsidized residents, Yentel added.

“He has proposed evicting 100,000 people, including 55,000 American children, from subsidized housing – in California, over 37,000 of the lowest-income people are at risk of eviction from this Trump proposal alone. He’s proposed allowing homeless shelters to discriminate and refuse shelter to transgender and other LGBTQ people, subjecting them to high risk of violence.”

Trump has long struggled to combat Pelosi, who last week led House Democrats to impeach him over abuse of power and obstruction of Congress. Even his tried and trusted method of branding adversaries has eluded him, with “Nervous Nancy” failing to stick and now “Crazy Nancy” being floated.

But not for the first time, he has latched on to an attack line that draws on headlines and talking points to build a superficial case in the eyes of his partisan supporters. The rocketing cost of housing, wrangling over over affordable construction, legal complications, substance abuse and mental health issues have contributed to a surge of homelessness in San Francisco, Los Angeles and other parts of California.

Earlier this month the Department of Housing and Urban Development, led by secretary Ben Carson, reported that homelessness in the US has grown for a third consecutive year. “Homelessness increased in California by 21,306 people, or 16.4%, accounting for more than the entire national increase,” the department said.

Facebook Twitter Pinterest Homelessness is on the rise in San Francisco and other California cities. Photograph: Alamy Stock Photo

In response, California’s governor, Gavin Newsom, told the Associated Press that California has invested a record $1bn to help communities fight homelessness. He added: “But we have work to do. And we need the federal government to do its part.”

The federal government, however, has alarmed the NLIHC and other advocates for homeless people. Earlier this month the White House appointed Robert Marbut as director of the United States Interagency Council on Homelessness, which works with 19 federal departments and agencies.

The New York Times noted: “Marbut has worked with cities in states such as California and Florida to build homeless shelters equipped with job training, mental health services, and other support services. His shelters often have an outside courtyard where people who have broken rules are told to sleep.”

Marbut is an opponent of “Housing First”, a research-backed strategy that prioritizes finding safe, stable and accessible housing for people experiencing homelessness, and that campaigners say has worked well in many cities. Critics fear that Marbut will criminalize much of the behavior associated with homelessness.

With its Democratic leanings and so-called “Hollywood elites”, California has become a punching bag for Trump. On an otherwise quiet Christmas Day, he railed against the state’s governor, Gavin Newsom, whom he claimed had “done a really bad job on taking care of the homeless population in California. If he can’t fix the problem, the Federal Govt. will get involved!”

In his barrage of tweets against Pelosi on Thursday, Trump added: “… she has lost total control and, along with her equally incompetent governor, Gavin Newsom, it is a very sad sight!”

Newsom, a former mayor of San Francisco who frequently jabs back at the current president, tweeted in response: “I imagine Trump’s Christmas to be like that scene when the Grinch yells ‘I’m an idiot!’” and his echo yells back ‘you’re an idiot!!’”