Mark Melancon, who pitched well for the Nationals last season after arriving at the trade deadline, signed a four-year deal with San Francisco. (Katherine Frey/The Washington Post)

Many times, Washington Nationals General Manager Mike Rizzo has shuffled a few feet one way or another and reminded scrums of reporters about the dangers of standing with one’s back to the wall. He always smiles, but he never fails to move, so truth always glimmers through his joke: Rizzo refuses to be cornered, spatially and otherwise, always looking for a way out.

So when facing a larger-than-normal media horde Monday on the first day of baseball’s winter meetings, held a quick drive from Nationals Park, Rizzo made sure to give himself a buffer between him and the Nationals background propped up for the cameras on the 11th floor of the Gaylord National Resort and Convention Center.

When asked about what his team will do now that former closer Mark Melancon rejected his Nationals offer and signed with the San Francisco Giants, Rizzo avoided specific alternatives but was adamant that his team has plenty.

“We’ve gotten a lot of good in-house candidates [to close]. We feel that we have a deep, talented bullpen,” he said. “But our adage over here is that you never have enough pitching, and the bullpen is something that we’re going to have to address.”

The Nationals chased Melancon, enamored with his clubhouse presence and reliability. He took a four-year deal worth $62 million from the Giants. Rizzo did not outline terms Monday, but a person familiar with the Nationals’ dealings said they made a four-year offer for less than $60 million.

“It’s just at the end of the day, the Giants offered him more,” Rizzo said, “and he took the deal.”

No tears shed, no bridges burned — but no closer either. So now what? Well, as usual, Rizzo pointed to contingency plans. The Nationals have “a lot of lines in the water,” he said, “a lot of irons in the fire” to improve. Do any of those lines lead to an elite closer?

As has been well documented, three elite closers highlight this year’s free agent market: Aroldis Chapman, Kenley Jansen and Melancon. The Nationals were outbid for the cheapest of the three.

Chapman reportedly wants a six-year deal, and whether or not that is realistic, he seems likely to get significantly more than the $15 million-plus Melancon will make annually. Jansen seems certain to get more, too — perhaps as much as $20 million per year. Plus, the Los Angeles Dodgers made Jansen a qualifying offer. Signing him not only requires exorbitant amounts but a first-round draft pick, too. Does the fact that they could not afford Melancon mean the Nationals are out of the running for the other two?

“We’re going to allocate our resources in the best way we possibly can. And if that’s a closer, that’s fine. If it’s another position, that’s fine,” Rizzo said. “We’re going to give ourselves the best chance to get an impactful player at the right price and use our dollars the best way we can.”

Rizzo said at the beginning of the offseason that he planned to talk to Chapman’s representatives, and he has spoken to Jansen’s agent, too. The Nationals have long liked Chapman, a Dusty Baker favorite, and went so far as to do their own research on his domestic violence incident last offseason. But they would be bidding against titans such as the Dodgers, the New York Yankees and perhaps even the financially unpredictable Miami Marlins for both pitchers. The trade market could be more beneficial.

The Nationals targeted Kansas City closer Wade Davis, a free agent after the 2017 season, at the trade deadline but eventually settled on Melancon, in part because of concerns about Davis’s health. The Royals placed Davis on the disabled list a few hours before the Melancon deal became official. Now healthy, Davis could be an option for the Nationals, who have plenty of prospect pieces at a variety of levels from which to deal.

Reports suggest the Marlins are pursuing one of the big three closers, though they have a hard-throwing closer already in A.J. Ramos. Should they sign Chapman or Jansen, perhaps Ramos could become a possibility for the Nationals.

The Tampa Bay Rays are shopping several of their pitchers, according to reports, so their closer, Alex Colome, could fit. The Chicago White Sox seem willing to sell almost anyone, which would include closer David Robertson. Colome and Robertson would likely not have the same game-changing impact as Jansen or Chapman — but they would not require the same franchise-altering investment, either.

Similarly, the Nationals scouted former Royals closer Greg Holland, who missed last season after Tommy John surgery. Holland, a Scott Boras client, was throwing in the low 90s at a well-attended showcase for scouts last month, and one person familiar with his situation said the Nationals have expressed interest.

Holland would come with a lesser price tag than one of the big-name closers but with higher risk, too. Then again, the Nationals do not shy away from pitchers who have had Tommy John surgery and in fact have made a habit of finding value in them as other teams shy away.

Former Arizona Diamondbacks closer Brad Ziegler and former Texas Rangers closer Neftali Feliz would be low-cost free agents, likely more suited to bolster the seventh or eighth inning than the ninth. Koda Glover struggled in his first major league stint, but he was pitching through a hip injury until the Nationals shut him down in mid-September. Glover, Blake Treinen, Sammy Solis and others are among those “in-house candidates” to which Rizzo referred.