A Capitals player takes the ice before playing the Winnipeg Jets at Verizon Center on Feb. 6. (Patrick Smith/Getty Images)

After placing playoff races and divisional rivalries on hold for nearly three weeks in favor of national pride, the NHL is rousing from its Olympics-induced slumber. The flame has been extinguished in Sochi, players are on their way back to their North American teams and there’s little time to waste.

The NHL’s regular season resumes Tuesday — the Washington Capitals’ first game back is Thursday — and less than seven weeks remain for teams to separate themselves from the pack and reach the Stanley Cup playoffs.

One of six teams within three points of the last wild-card spot in the Eastern Conference, the Capitals have little room for error over the final 23 games, but General Manager George McPhee says he believes this group will find its way to the playoffs for a seventh straight year.

“It’s a team that hasn’t played its best hockey yet. I thought we were starting to play well before the break,” McPhee said. “Hopefully when we come out of the break we’ll be healthy and play the way I think they’re capable and they think they’re capable of playing. . . . We’ve been in this situation before. We’ve got to play well down the stretch, and it’s time.”

But in order to reach the postseason, the Capitals have a variety of challenges to overcome.

While Washington expects Mike Green and Mikhail Grabovski back in the lineup Thursday in Florida after they missed time before the Olympic break with a concussion and sprained left ankle, respectively, there’s uncertainty about those who didn’t have time to rest over the past few weeks.

The team’s five Olympians return to Washington experiencing varying levels of disappointment. Martin Erat’s Czech squad was bounced in the quarterfinals, and John Carlson and the United States fell flat in their final two games and left Sochi having finished in fourth place.

Marcus Johansson earned a silver medal with Sweden, but his countryman and Capitals top center Nicklas Backstrom was pulled from the lineup for the gold medal game after testing positive for a banned substance that is found in his allergy medication. It’s unknown if Backstrom will receive a silver medal.

Alex Ovechkin received much of the blame for Russia being unceremoniously knocked out in the quarterfinals, and while he was dealing with that disappointment he unexpectedly had to cope with his father undergoing heart surgery as well.

“The toughest thing is obviously going to be Ovi and where his head is, which I think we can all say we don’t blame him,” Coach Adam Oates said. “I’ll try to get him back on page as fast as I can. . . . He might be down for a bit. Maybe he can shake it off, who knows.”

Then there’s the simple math. Washington is in the mix for a playoff spot, but doesn’t own the tiebreaker against any other team in the race because the Capitals have won only 19 of their 59 games in regulation or overtime — sixth fewest in the league. That means they will likely need to completely surpass teams in the standings to get in.

Players insist they aren’t overanalyzing the standings picture just yet.

“I don’t really look at it, because then you get wishing and hoping that whoever loses,” forward Joel Ward said. “You know there are going to be a lot of overtimes, shootouts, teams are going to be getting points. We’ve just got to find a way to win games regardless how you do it.”

In all but one of the past seven full 82-game seasons, teams have needed at least 92 points to reach the playoffs in the Eastern Conference. The Capitals would need to obtain 29 points in their final 23 games to hit that projected cutoff point, which means they will have to gain slightly more than six out of every 10 points available to them.

Through the first 59 games, though, Washington has captured just more than five out of every 10 points available. To make up that difference the Capitals will need a significant uptick in their overall play; they haven’t won three games in a row since early December.

Their remaining schedule is one of the toughest in the league, with only two games against teams that sit more than four points out of the final playoff spot in their conference. Eleven of Washington’s final 23 games come against teams currently ranked in the top 10 in the league in points.

“Sometimes that can be a benefit. Sometimes you play those teams that are lower in the standings, they’re tough to get up for,” forward Eric Fehr said. “These games won’t be tough to get up for. They’re really good teams, some of our rivals, so we’re going to have to bring our A-game. If we can pull it off, it will benefit us a lot going towards playoffs.”

They face Eastern Conference-leading Pittsburgh twice, second-place Boston three times and each of the top four Western Conference teams — Anaheim, St. Louis, Chicago and San Jose — once along with two meetings each against tough teams looking to hang on to playoff spots in Philadelphia and Los Angeles.

“We have a tough schedule, everybody has a tough schedule,” McPhee said. “Let’s find out what we’re made of.”