The Lions depart for South Africa next Sunday (May 24) with their first tour match taking place six days later against a Royal XV in Rustenberg.
The tourists then play a further five provincial fixtures before taking on the world champion Springboks in Durban, Pretoria and Johannesburg on June 20, 27 and July 4 respectively.
"This week is about us getting together as a group of people but also having a strong rugby focus," said head coach McGeechan.
"This is the shortest Lions tour in history with the shortest amount of time leading up to the Test series.
"In only four weeks on Saturday we're playing the first Test so everything we do has to be to try and get ourselves in the right shape.
"Part of that is getting to know each other as a group and the other part is getting to know how we want to play, what we want to do and what we want to be about."
McGeechan's first experience as a Lion came on the Lions' historic 1974 tour of South Africa but the Scot admits he still has the same sense of excitement ahead what will be his fifth tour as a player or coach some 35 years later.
"The body might look slightly more ragged but inside I don't feel any different," he added.
"The Lions is a privilege and it's unique. To be involved in that is a fantastic opportunity and experience. There isn't anything bigger than this."
Tour captain Paul O'Connell echoed his coach's sentiments, suggesting that creating the unique team spirit associated with the Lions will play a key role both in the run up to departure for South Africa and during the tour itself.
"First and foremost, the talent is here," explained O'Connell, who will be embarking on his second successive tour following the 2005 series in New Zealand.
"The coaching staff have very good ideas on how we want to play and how we want to perform.
"I think all those bits are going to be ticked off so it's about us coming together as a team.
"We really have to work on coming together as a team in a short space of time. If we can do that then we'll have a very good chance in South Africa."
McGeechan also announced that he will not be naming a replacement for Welsh centre Tom Shanklin, who was ruled out of the tour through injury almost a fortnight ago.
Shanklin requires surgery on a dislocated shoulder but McGeechan has decided to keep the squad at 36 in order to give his players as much game-time as possible in the lead up to the Test series.
"When we selected the extra player back in April, we were trying to cover all the bases," McGeechan explained.
"We faced the possibility that we might be without 14 players involved in the Heineken Cup final going into the early part of the tour.
"As it's transpired, the first two games in particular we can cover with the squad that we have.
"It's now about giving the opportunity to the players who are there to have that chance and game-time."
Euan Murray and Alan Quinlan were the only players missing from today's squad meeting, with the Munster flanker having been suspended for 12 weeks following an ERC disciplinary hearing last week and the Northampton prop having not been released by his club.
McGeechan and tour manager Gerald Davies explained that the Lions will not stand in the way of Quinlan's intended appeal, although McGeechan announced that he did know who would replace the Irishman if his appeal was dismissed.
Players from Heineken Cup finalists Leicester Tigers and Leinster were all present and will return to their respective teams this evening but the Lions were told this morning that Murray would not be present.
"We were informed this morning by Northampton that Euan Murray will not be released," said Davies.
"We informed the Unions of our plans for this week back in the autumn and no one responded to say that they disagreed with those plans.
"We did emphasise that there would be no training whatsoever today and that players would be released back to those clubs involved in the two finals by 6pm this evening.
"Euan will be joining us after the European Challenge Cup final at the weekend. We are very disappointed with that."