D.C. Council Chairman Kwame R. Brown is adding photos to the office wall on which he displays a collage of images from his term as chairman. His staff is booking speaking engagements and other events through October. In September, Brown will represent the District as a delegate to the Democratic National Convention.

He’s working 15-hour days and gets energy from the bin of dried fruit and fiber bars near the desk of one of his budget analysts. He needed a quick jolt Wednesday as he prepared to meet with Mayor Vincent C. Gray (D) to finalize the city’s fiscal 2013 budget, which is up for a vote this week.

It’s not an easy time for Brown, whose future is the subject of rampant speculation as he awaits the outcome of a federal investigation into his finances and his 2008 campaign. Federal officials say the long-running investigation has been intensifying and is entering its final stages. The officials spoke on condition of anonymity because they are not authorized to speak publicly.

But Brown remains upbeat. He says he is tired of worrying about rumors and thinks that he is only now reaching his potential as a leader.

“I’m not worried one bit,” Brown said of the federal investigation last week, as he allowed a Washington Post reporter to shadow him. “I am just 100 percent focused on doing what I am doing.”

In the past month, a federal judge has sentenced former council member Harry Thomas Jr. (D-Ward 5) to prison for stealing from the city, and two former campaign aides to Mayor Vincent C. Gray have pleaded guilty in a widening probe into the mayor’s 2010 election campaign.

But there has been little public movement on a third federal investigation hanging over the city, the year-old probe into whether Brown improperly benefited from $239,000 in campaign funds steered to a consulting firm run by his brother.

Some of Brown’s colleagues speculate that he won’t survive the summer, but Brown is forging ahead with his agenda.

“People are saying: ‘You stole all this money. You got all this money. You’ve got to resign,’ ” said Brown, surrounded in his wood-paneled office by his growing collection of Muhammad Ali memorabilia. “I don’t entertain that stuff.”

As Brown tries to maintain his focus on city business, his colleagues say he has been anything but weak.

“So far, I have seen no evidence that he is under any stress above and beyond what comes with the job,” council member David A. Catania (I-At large) said.

Brown got off to a rocky start because of the uproar over his requesting a city-leased, fully-loaded sport-utility vehicle, which he has long-since returned. But in the meantime, he has grown into the job, exerting more control and racking up legislative victories.

On Tuesday, the council is expected to give unanimous final approval to a Brown-negotiated fiscal 2013 budget that includes no new taxes, $18 million for affordable housing, money for 20 new or refurbished parks and playgrounds, and money for changes intended to improve middle schools.

“He has shown extraordinary skill,” said council member Jim Graham (D-Ward 1). “When he puts his mind to something, he gets it, even big things.”

At the top of his game legislatively, Brown is quietly reaching out, trying to keep his record from being overshadowed by the investigation.

On Friday morning, Brown privately met with the D.C. Business Coalition, a group of about three dozen influential leaders who meet informally to discuss District affairs. Several members said they had never seen Brown more focused as he discussed the budget, his vision for the city and the area’s booming real estate market.

“We are a tough, well-informed audience,” said W. Shaun Parr, vice president for government affairs of the Apartment and Office Building Association of Metropolitan Washington. “Nobody is going to buy his BS, and his point was [that the District] never missed a beat, despite everything that has happened, and we agree with him.”

But Brown is a long way from shaking allegations growing out of his 2008 campaign, when he was running for reelection as an at-large member.

The U.S. attorney’s office launched its probe last spring after the city’s Office of Campaign Finance released an audit that showed that Brown’s campaign had failed to report the raising and spending of more than $270,000.

The audit also turned up the $239,000 that had been passed along to the now-defunct consulting firm run by Brown’s brother Che. In a subsequent complaint, the Campaign Finance Office alleged that the campaign had failed to register a $60,000 bank account that Che Brown controlled.

Brown’s father, Marshall, a veteran political organizer, headed up the 2008 campaign, which raised nearly $1 million, despite Brown’s facing nominal opposition.

About the same time, Brown was experiencing financial difficulties. By 2010, he was about $700,000 in debt, which resulted in four lawsuits from credit card companies alleging nonpayment of about $50,000.

Brown, who said the financial stresses stemmed from his efforts to raise a young family in the District, has since paid off the credit card debt.

Experts say it’s not illegal for a candidate to hire a family member, but investigators are exploring whether Brown or his family benefited illegally from the campaign.

A. Scott Bolden, an attorney for Che Brown, said his client is cooperating and would fight any charges that might be brought against him.

“We have turned over a significant number of documents, and we are prepared to defend those documents and have defended those documents,” Bolden said. “No money from the 2008 campaign was misappropriated or subject to any unlawful, illegal or inappropriate conduct on the part of Che Brown.”

Troy W. Poole, an attorney for Marshall Brown, said his “client did not break any kind of campaign laws or any other laws that they may be investigating.”

Poole also said, “My client has not been offered any kind of deal, nor are we looking for any kind of deal.”

Attorneys for the three Browns have entered into a “joint defense agreement,” in which they share information and defense strategies.

Kwame Brown would not discuss specifics of the investigation, but he said he is tired of people talking about it. He noted that the allegations surfaced during the 2010 race for council chairman against council member Vincent B. Orange (D-At large).

“Since Vincent Orange started this process and council member Orange spread this . . . I’ve just kept moving, “ Brown said. “No one has come up to me and said, ‘Mr. Chairman, you are not doing your job.’”

On Wednesday, Brown presided at a hearing on home rule, met with Gray and attended the swearing in of newly elected council member Kenyan R. McDuffie (D-Ward 5). He capped the day by hosting an annual awards ceremony for most-improved high school seniors, a program he started six years ago.

Brown told the students that he was an average student in high school but had caught a few lucky breaks. He also said they should work hard, stay focused and not let detractors bring them down.

“From day one, there were always people who would love to see me fail,” Brown said in an interview. “If I stopped and thought why someone didn’t believe in me, I would just spend a lot of time thinking.”