Eight months into President Biden’s term, both he and Jill Biden, the first lady, are finding that winning the “battle for the soul of the nation” is perhaps his most elusive campaign promise. In Washington, an outrage-driven approach to politics has replaced Mr. Biden’s rose-colored belief that bipartisan deal making can be an art form. As he tries to prove that this is still possible, his wife is not a bystander.

Dr. Biden, an English and writing professor who made history as the only first lady to keep her career while in the White House, has traveled to 32 states, many of them conservative, to promote school reopenings, infrastructure funding, community colleges and support for military families. She has also traveled to states where low numbers of eligible people have received the coronavirus vaccine.

“He trusts my intuition as a spouse,” Dr. Biden said in the interview, “not as a policy person or an adviser.”

Dr. Biden entered the White House with several focus areas, including supporting free community college. The president said this spring that she would be “deeply involved” in the effort to make community college tuition free. So far, she is not deeply engaged in the legislative or policy arenas. After The Times published its profile of Dr. Biden on Sunday evening, Elizabeth Alexander, her communications director, said that the first lady’s work to raise awareness on the issue “is a big reason why it’s in the legislative package today.”

They are sometimes confronted with the reality that Mr. Biden’s decisions have been politically costly. When the first couple met with Gold Star families after a terrorist attack in Kabul last month, some relatives made it a point to publicly embrace former President Donald J. Trump.

Neither Biden takes an overly optimistic view that the country’s problems are easily solvable, their advisers say, but both are united in the idea that Mr. Biden is the best-positioned person to try.

“She very much believed he was the right person for the time,” Mike Donilon, one of the couple’s closest advisers, said in an interview. He said that when it came time to make “fundamental decisions about the campaign message and strategy, she was there, and she really brought it to a close.”