Republican Larry Hogan joins supporters waving signs in Bowie, Md., on Election Day. He won the governorship in an upset. (Mark Gail/For The Washington Post)

— Standing behind the counter of a preppy boutique, Maryland Comptroller Peter Franchot (D) presented Gov.-elect Larry Hogan (R) with one of his office’s signature medallions.

“Wow,” Hogan said, turning the coin over in his hand. “That is very thoughtful. . . . I don’t have any medallions to give you back. I’m going to think of something.”

“You can buy a round of beer tonight,” Franchot said.

“Okay,” Hogan laughed. “I will buy you a beer.”

And that cemented Hogan’s least surprising, but possibly most powerful, cross-party-lines alliance. Once Hogan takes office Jan. 21, he and Franchot will hold two of the three seats on the Board of Public Works, which approves most of the state’s major purchases.

Hogan pitched himself to voters as a businessman who can control state spending and cut waste without diminishing services, then pass along the savings to struggling taxpayers. To cut taxes, he will have to work with a Democrat-dominated legislature . But the governor wields great power over the state budget, and, if he can get a second vote, decisions made by the Board of Public Works.

Franchot is a fiscally conservative Democrat from Takoma Park who became the state’s top tax collector eight years ago, as Gov. Martin O’Malley (D) took office. Although both are Democrats, Franchot and O’Malley have publicly clashed numerous times. When Franchot criticized O’Malley for wanting to raise the gas tax in 2012, the governor snipped: “He’s kind of our version of Mitt Romney; I mean, he’s very happy taking opposite sides of every issue and always has throughout his career.”

Franchot, a former state delegate, is known to give long lectures on fiscal responsibility during board meetings, often while the governor taps away on his iPad, looking annoyed. Earlier this year, as O’Malley and other Democrats tried to recover from the embarrassment of a failed health insurance Web site, Franchot questioned the process by which Maryland hired a North Dakota company to build a site that crashed on its first day and has cost at least $50 million to replace.

But Public Works Board meetings often follow this script: Franchot raises concerns about the cost, procurement or details of a project, and then O’Malley and Treasurer Nancy K. Kopp (D) vote to approve it anyway.

With Hogan on the board, that could change. Although Franchot endorsed fellow Democrat Lt. Gov. Anthony G. Brown in the governor’s race, it’s clear that his fiscal views are often closer to those of the Republican. Taxes, state spending and the economy became the leading issues of the race, and Brown often struggled to defend the O’Malley administration’s record. Soon after the election, Hogan visited Franchot in his office for a conversation that both speak glowingly of, although they note that it lacked specifics.

“I think it’s a new day for the Board of Public Works,” Franchot said Monday. “We don’t have to do anything draconian, but we need much better financial management of the state’s spending and borrowing.”

Franchot invited the governor-elect to join him on the Eastern Shore on Monday to visit and promote small businesses. The two were quite chummy as they walked the streets of downtown Easton. They sang several rounds of “Jingle Bells” with Santa Claus. At MayaBella’s Pizzeria, Hogan bought the comptroller a root beer. And during an interview with a local television station, Hogan pulled Franchot into the shot.

“I got to tell you, we agree on a lot more things than we disagree on, even though we come from different parties,” Hogan said of his new friend as they visited Sailor, the preppy boutique. “I think you’re going to find, more often than not, instead of having one vote on the Board of Public Works, we might have two once in a while and actually get things done.”

That prompted Nick Panuzio, chairman of the Talbot County Republican Central Committee, to slyly tell Franchot: “Would love to have you join us.”

Hogan laughed and said: “I’ll try to work on him.” (The joke didn’t end there, with Hogan later offering to buy the comptroller a phone cover decorated with pink and green elephants.)

During their last stop at Irish Traditions, where Hogan’s wife, Yumi Hogan, bought her husband a tie to wear on St. Patrick’s Day, the governor-elect told Franchot that when his staff posted an article about their upcoming shopping trip on Facebook, he received a slew of comments from Marylanders who voted for the Republican for governor and the Democrat for comptroller. Franchot nodded.

It’s no secret that Franchot has thought about running for governor himself — and some have wondered if he might try in 2018, when Hogan’s first term ends. Franchot dismissed the suggestion on Monday.

“For the next two years, the emphasis is on governing and getting the job done,” Franchot said after visiting Precision Printing and Embroidery. “The rhetoric and the spin and the promises of campaigns that have been made, please, God, put them behind us. And let’s just roll up our sleeves and get the job done.”