In 2007, a Pennsylvania state representative named Josh Shapiro broke with much of the Democratic establishment to back for president a first-term senator from Illinois named Barack Obama.

Mr. Obama, who lost Pennsylvania’s 2008 primary to Hillary Clinton but won the presidency, did not forget it.

Over the nearly two decades since that early endorsement, Mr. Shapiro and Mr. Obama remained in touch, developing a connection that is closer than is commonly understood, according to interviews with people who know them both. Now, Mr. Shapiro is a popular governor in a crucial battleground state who could join a presidential ticket himself, as Vice President Kamala Harris, another early Obama supporter, weighs her running-mate options.

The relationship between the two men offers a window into the ins

tincts and influences of one of Ms. Harris’s top choices.

“Josh was one of our earliest supporters in 2008 in Pennsylvania, when almost all the political establishment was with Hillary,” David Plouffe, who managed Mr. Obama’s campaign that year, said in a text message on Thursday. (Separately, on Friday, the Harris campaign announced that Mr. Plouffe had joined as a senior adviser.)

“They spent a lot of time together, and Obama thought from Day 1 he had a super high political ceiling,” Mr. Plouffe added. “He stuck with us during the bad times, including us getting pummeled in his home state, and never shied from a single thing we asked him to do.”

Over the past year, heading into a pivotal presidential election, they have spent time together in person, and the governor continues to seek Mr. Obama’s advice, according to a person with knowledge of the relationship who insisted on anonymity to describe private conversations.

Certainly, Mr. Obama knows and has supported other vice-presidential contenders over their careers, including Gov. Tim Walz of Minnesota and Senator Mark Kelly of Arizona. A person close to Mr. Obama said the former president seeks to be a sounding board and confidant for Ms. Harris. But the person, who was also granted anonymity to discuss private conversations, did not expect Mr. Obama to put a thumb on the scale for any vice-presidential contender.

It is not clear where Mr. Shapiro’s candidacy stands in Ms. Harris’s eyes, as he faces growing scrutiny in the national spotlight, and criticism from some on the political left. Mr. Shapiro, along with Mr. Walz and Mr. Kelly, is scheduled to meet with Ms. Harris on Sunday at her residence in Washington, D.C., The Times reported.

Mr. Shapiro described Mr. Obama as someone “whose example I’ve tried to emulate” in an interview last week, but he declined to comment on “any communications that I have with President Obama.”

Some have suggested — sometimes lightheartedly, sometimes mockingly — that Mr. Shapiro has taken his goal of emulating Mr. Obama’s example literally.

Among the likenesses: They both managed to end up with family dogs named “Bo.” And Mr. Shapiro’s cadence, rhythms and sometimes even hand gestures can seem so reminiscent of the former president’s that some people have started jokingly referring online to Mr. Shapiro, who is Jewish, as “Baruch Obama.”

Highlighting the similarities, “The Daily Show” questioned whether Mr. Shapiro was “doing an Obama.” Former President Donald J. Trump’s running mate, Senator JD Vance of Ohio, suggested recently that Mr. Shapiro “talks like Barack Obama. It’s like if I tried to do a really bad impression of Barack Obama.”