D.C. mayor-elect Muriel Bowser participates in her final city council meeting Wednesday. (Jonathan Newton/The Washington Post)

The District’s incoming Democratic mayor and the Utah Republican soon to assume congressional oversight of D.C. affairs agree on this bipartisan goal: It would be great to bring the Olympics to Washington.

“What a great thing it would be for the nation,” Rep. Jason Chaffetz said he told Mayor-elect Muriel E. Bowser.

The prospect of bringing the 2024 Summer Games to the city was one of the topics covered during a 20-minute get-to-know-you session Wednesday morning on Capitol Hill between Bowser, who assumes the mayoralty Jan. 2, and the incoming chairman of the powerful House Oversight and Government Reform Committee.

Chaffetz said in an interview that he would not only support the D.C. bid for the 2024 Games — having seen the impact of the 2002 Winter Games on Utah — but would urge Republicans in Congress to spend federal funds in support of a successful Olympics in the nation’s capital.

“Clearly, it is a national event, and it would be appropriate, as it was in Salt Lake [City], for federal funds to be injected,” Chaffetz said. “It’s very difficult to pull it off otherwise.”

“The world’s eyes would be focused on the United States for weeks on end, and I think it’s in the best interest of the country, and I would be supportive of spending those moneys,” he continued. “Exactly what they would be used for, that’s something we would have to flesh out.”

The meeting came a day after Bowser joined the leaders of the D.C. 2024 bid committee in Northern California for a presentation to the U.S. Olympic Committee, which is expected to select a U.S. city next month to put forward as the official American bid.

“My ‘spidey sense’ tells me that we’re in good shape,” Bowser said Wednesday. “When I got involved in this, everybody believed we were running second against Los Angeles. We expected they had a very strong proposal as well, but I think we definitely put our best foot forward.”

“When we looked around that room, there were a lot of nodding heads,” she continued. “They want an American city to be chosen, so they want to make sure that the American city is well-positioned. . . . We’re used to putting on national security events; we can move the people; we have a lot of existing facilities and infrastructure. We put on a good case for D.C. being the American city.”

Bowser said she appreciated Chaffetz’s offer to drum up congressional support: “We’re going to need the federal government, I’m sure.”

The International Olympic Committee is scheduled to select the location for the 2024 Summer Games in September 2016.

Wednesday’s meeting between Chaffetz and Bowser kicked off what could be a critical relationship for the incoming mayor, who will take office as a new, GOP-controlled Congress prepares to be sworn in — and with new indications that the city’s liberal policymaking could be getting a closer look from the Hill.

Last week, Congress passed a spending bill that included language preventing the District from taking steps to liberalize recreational marijuana use.

Republican leaders say the language is intended to block implementation of a legalization referendum passed by 65 percent of D.C. voters Nov. 4. But some Democrats and city officials say there is room in that language to allow the measure to take effect.

Bowser and Chaffetz said the marijuana measure did not come up in their meeting Wednesday.

Asked why she did not raise the subject, Bowser said, “We had a meet-and-greet to discuss how we’re going to continue to work together.”

“It was a wee bit early in the morning to talk about marijuana,” Chaffetz said of the 8:45 a.m. meeting.

Still, the marijuana issue threatens to become a flash point in city-federal relations.

Bowser has signaled that she will support efforts to keep pushing the pot initiative forward. And Chaffetz said he believes the budget language clearly blocks the city from moving forward with legalization. “That issue has come and gone,” he said.

D.C. Council Chairman Phil Mendelson (D) said he plans to send the referendum to Congress for a mandatory review period, but Chaffetz said he would not seek to intervene at that point. “It’s already been dealt with,” he said. “It’s crystal clear in the law.”

More likely, Chaffetz said, would be court action forcing the city to enforce the congressional rider: “I don’t know what sort of legal moves someone might try to make from the city, but I think it would be ill-advised and fruitless. There are a lot of other things to work on for the city.”

Any standoff, however, will come another day. In interviews after their meeting, both Bowser and Chaffetz traded pleasantries and pledges to communicate.

Bowser said they shared cellphone numbers: “He seems to be like me — likes to have direct contact.”

“We know his politics, and he knows ours, and he also knows that he has a responsibility, and we have a responsibility,” she continued. “So I expect that we’ll have a professional dialogue. . . . We’re all going to talk to each other, and we’re not going to act as though the other doesn’t exist.”