The first lady, Jill Biden, complained about her husband’s choice of Kamala Harris as running mate and now vice-president, according to a new book, asking: “There are millions of people in the United States. Why … do we have to choose the one who attacked Joe?”

The quote is contained in This Will Not Pass: Trump, Biden, and the Battle for America’s Future, by the New York Times reporters Jonathan Martin and Alex Burns, which is due to be published on 3 May.

Excerpts have already been reported. Jill Biden’s reported remark was relayed by Politico on Tuesday.

Harris made her mark in the Democratic primary – and bruised Biden – at a debate in Miami in June 2019, criticising his opposition to bussing, a way of racially integrating public schools, as a young senator in the 1970s.

Biden was reportedly hurt by the insinuation he had been racist but still picked the California senator as his running mate and ultimately the first woman and person of color to be vice-president.

A spokesman for Jill Biden, Michael Larosa, told Politico: “Many books will be written on the 2020 campaign, with countless retellings of events – some accurate, some inaccurate. The first lady and her team do not plan to comment on any of them.”

Promising “juicy excerpts” of the new politics book, Politico said Martin and Burns offer extensive accounts of Harris’s struggles as vice-president. As allies complained about her “impossible” portfolio, including border security, the news website said, “Kate Bedingfield, Biden’s communications director, not only grew tired of the criticism that the White House was mismanaging Harris – she blamed the VP.”

Martin and Burnswrite: “In private, Bedingfield had taken to noting that the vice-presidency was not the first time in Harris’s political career that she had fallen short of sky-high expectations: her Senate office had been messy and her presidential campaign had been a fiasco. Perhaps, she suggested, the problem was not the vice-president’s staff.”

Bedingfield told Politico: “The fact that no one working on this book bothered to call to fact-check this unattributed claim tells you what you need to know. Vice-President Harris is a force in this administration and I have the utmost respect for the work she does every day to move the country forward.”

Harris, the book says, does not want only to work on issues connected to women and Black Americans. In her attempts to lead the way on voting rights, however, she reportedly felt stymied by Biden’s reluctance to commit to serious Senate reform.

Burns and Martin also report that Biden and Harris are “friendly but not close”, but say the president grew frustrated with leaks about Harris, warning aides that if “he found that any of them was stirring up negative stories about the vice-president … they would quickly be former staff”.

The authors say Harris’s frustration was “up in the stratosphere”, according to an unnamed senator who “lamented that Harris’s political decline was a ‘slow-rolling Greek tragedy’. Her approval numbers were even lower than Biden’s, and other Democrats were already eyeing the 2024 race if Biden declined to run.”

Biden, the oldest president ever inaugurated for the first time, will turn 82 shortly after the 2024 election. He has said he intends to run again.

Whatever the accuracy of the reporting by Martin and Burns, it seems Harris may have cause to agree with a famous judgment by John Nance Garner, vice-president to Franklin D Roosevelt from 1933 to 1941. The vice-presidency, Garner said, “wasn’t worth a bucket of warm piss”.