TAMPA, Fla. -- Carey Price and Stephane Waite huddled around the goalie coach’s computer before practice Monday. The Montreal Canadiens franchise goalie was looking at clips, always searching for ways to improve his craft.

He’ll need to be near perfect again Tuesday night at Amalie Arena, as the Canadiens try to avoid elimination for a third straight game in their Eastern Conference semifinal series. Game time is 7:30 ET.

The Tampa Bay Lightning lit Price up for six goals in Game 2, but it has been two or fewer a game ever since, with the Hart Trophy and Vezina Trophy finalist very much finding his groove.

What Price no longer has to do is prove much to anyone. He already has his admirers around the league.

"He’s the best player in the National Hockey League," Detroit Red Wings coach Mike Babcock told ESPN.com over the phone Monday. "To me, who has more an impact in the National Hockey League than Carey Price?"

There was much debate heading into the 2014 Sochi Olympics whether Team Canada should go with incumbent veteran Roberto Luongo, who helped Canada to gold in Vancouver in 2010, or turn to the younger Price.

While Babcock, Canada’s coach in Sochi, kept the media guessing even a few games into the tournament, it turns out his mind basically was made up much earlier.

"I remember having a good meeting. Jonathan Toews was there with P.K. Subban and Carey Price at Joey Tomato’s one night in Calgary," Babcock said of an Olympic training camp meeting. "We were having a social. We were talking about being a pro, asking Toews questions about what you do to separate yourself from the group, the leadership qualities. I remember having that talk at camp. Then I watched Carey that fall, and I just felt he was the guy."

Price’s recollection of the meeting with Babcock in Calgary was a simpler one.

"He’s a very straightforward coach. There’s no B.S. with him. You know where you stand," Price said Monday. "I got a lot of respect for him. Our meeting was very straightforward. He said: 'I just need a goaltender I can depend on.' It was pretty cut and dry. Having that [conversation] was really nice."

Since giving up six goals in Game 2, Carey Price hasn't given up more than two goals in a game. Mike Carlson/Getty Images

Price didn’t need to steal any games in Sochi. A powerful Canadian lineup rolled to a gold medal, but Price was cool as a cucumber and played his part perfectly.

"At the Olympics Games, I mean ... the guy is smooth, he’s square, he’s confident, he’s big, he plays the puck, he’s a good guy to talk to, he gives you confidence," said Babcock. "I don’t know what else to tell you but he’s the best player in the National Hockey League."

Price made perhaps the best save of the playoffs Saturday night in Game 5, when Lightning center Valtterri Filppula was staring at what seemed like a sure goal, but his one-timer in what appeared to be an open side was partly deflected at the last moment by Price’s outstretched glove.

"He’s a great goalie all-around. He’s really calm, and you don’t see a lot of net," Filppula said Monday. "He makes key saves. That one was a great save -- he makes a lot of those. He doesn’t move too much. It feels like it’s tough to get him out of position. He stays in."

That save was the kind Dominik Hasek made routinely in his heyday. Dallas Stars coach Lindy Ruff, who coached Hasek during that era in Buffalo, got a firsthand glimpse of Price as part of the Canadian coaching staff in Sochi.

"Just like Dom, Carey makes the unbelievable saves look kind of routine, which is scary," Ruff told ESPN.com on Monday. "Dom would be ahead of the play, and Carey is the same way. He reads the play so well. He can be there for what we all think are unbelievable saves."

Ruff has already seen enough of the 27-year-old Price to not balk when asked to compare the two goalies.

"The mentality is the same," Ruff said. "To me, it seems like he wraps his arms around a pressure situation, and it doesn’t bother him at all. That was kind of Dom. He wanted that pressure situation, that big game. There’s no fear in their game. That’s pretty well what the best guys have. You can call it cocky, you can call it whatever you want to call it, but it’s a belief that they’re going to get it done."

You want belief? Price is now 7-0 in elimination games in the past two seasons, if you include the NHL playoffs (2-0 the past season and 2-0 so far this year) and the Olympics (quarterfinal, semifinal and gold-medal game).

Another NHL head coach, who requested anonymity Monday, said Price’s quiet confidence can play on the opposing team.

"The biggest strength this guy has is his ability to stay calm, no matter what," the coach said. "He is very laid-back, in a good way, shows confidence in his play, and I feel that can get in opposing team's heads.

"Not cocky but confident. I felt he was more cocky than confident early in his career, and that's what maturity can do for a goalie."

That maturity got a boost in Sochi. There, Price was surrounded by NHL captains galore, the likes of Toews, Sidney Crosby, Ryan Getzlaf and Shea Weber.

"Being able to see all those different leaders from different teams prepare for games, the calmness, the steadiness in the locker room beforehand and even during games, it was really fun to watch," Price said when asked what he gleaned from that experience.

In Montreal, there is no debate. Although the team still hasn’t named a captain since Brian Gionta left the past summer, everyone knows the No. 1 leader on the team.

But Price isn’t interested in trying the Luongo experiment from Vancouver, where the veteran goalie wore the captain "C" for a few seasons. That's just not a thing you see from an NHL goalie.

"Personally, I think the 'C' is more ceremonial than anything," Price said. "I don’t think you have to wear a letter to be a leader on a team. I’ve seen a lot of instances where maybe one guy was wearing the 'C' and maybe wasn’t as vocal as some other guys in the room. You don’t really need a letter to be a leader on the team."

No, you don’t. Not when you’re Carey Price.