Marsch's side will return from the two-week international break with Saturday's 3pm kick-off against the 11th-placed Saints who are heading to Elland Road having lost their last three league games.
Leeds, meanwhile, have savoured victories in their last two, a last-gasp 2-1 success at home to Norwich City followed by an incredible 3-2 triumph at Wolves in which United were 2-0 down and saw four players forced off injured.
The back-to-back wins have Marsch's side sat fifth-bottom and on 29 points ahead of today's return to action, United seven points clear of the drop zone but with all of the sides below them having games in hand.
Twenty nine points would technically speaking have been enough to stay up last term - a far cry from the usually well documented 40 point total from the 38 games on offer - but Marsch is instead focusing on continued hard work and growth from his hungry side.
Asked whether he had a figure in mind of the points tally that would make Leeds safe, Marsch reasoned: "I always heard it was a point a game because when I was with the US national team and I was an assistant, almost every American that we had in the Premier League was shooting for a point a game because they were always fighting relegation!
“But I don’t have a point total in mind.
“I’ve said it a lot and I’ll say it again, the focus is on the daily work and just trying to prepare ourselves and to grow as a group.
"The more that we do that, then I think the more that we can fight for points."
Providing an update on United's work during the two-week break, Marsch said: "We have been able to work through some tactical topics more and create better understanding with relationships in all phases of the game.
"I think that has been useful.
"We haven’t had everybody here or everybody on the pitch every day.
"But even the video sessions again and some of the guys coming back, we have just been updating them on some of the work that has been done and helping them understand the analysis that we have made over the last two weeks and then making sure that it can lead to a better and better performance, especially come Saturday.
"It is an eager group, hungry, hungry for more.
"I think we have to really maintain that mentality and understand that even though we have got six points and we have relieved some of the stress in terms of where we are in the table, that the best way to continue to control that is to make sure that we are really focused on every performance every day and maximising what we are doing.”
Saturday's visitors Southampton are five places and six points better off than Leeds who have also played one game more but Ralph Hasenhuttl's side have lost their last three games and last four in league and cup.
A 4-0 defeat at Aston Villa was followed by 2-1 home reverses against both Newcastle United and then Watford before a 4-1 loss against visiting Manchester City in the quarter-finals of the FA Cup.
Marsch, though, says there is more to Southampton's recent run than meets the eye.
"I’ve watched a lot of their recent matches and I think that they’ve been a little bit unlucky to not do better in some of these matches," warned the Whites boss.
“I thought what they did against Norwich, with and against the ball in their last victory or one of their last victories was quite good and they’ve developed I think a few more tactical nuances for how they like to rotate and move their specifically 6s around in build up phases.
"We’ll have to be aware of some of those things.
“We’ll have to understand that when they do create some rotations, how do we want to attack those positions in those moments?
“Obviously, we want to be effective in transition when we win balls but we have to also understand that one of the most important things is that we always have balance when we’re in possession so that we don’t allow their ball winnings to lead them into dangerous transition moments.
“We’ve talked already this week a lot about Southampton and what to expect and what we want to look like. It will be important.
“I’ve even talked a little bit with some of our front players, I like our front players to have a little bit of freedom sometimes to move around and find the game.
“But also we need to have a little bit more discipline to tactically and positionally be in the spots that we need, with and without the ball so that we can limit the opponent and also expose the opponent a little bit more.
"That’s been a talking point and I think all of those things will be really important against Southampton.
“It’s a similar philosophy that they like to play, it’s just the nuances of what they try to tactically do in different phases and what we like to do.”