The Jags skipper has been handed temporary control of first-team matters following the departures of Jackie McNamara and Simon Donnelly to Dundee United.
Archibald was denied his dugout debut last Saturday as Thistle's Irn-Bru First Division clash with Cowdenbeath was postponed due to a frozen Central Park pitch.
With a crucial double-header against Raith Rovers and title rivals Morton on the horizon, the pressure is on Archibald and No.2 Scott Paterson to deliver the title and Bannigan is confident the Jags squad will do their bit.
He said: "Hopefully we can win a few games for them and they can maybe stay on in the job.
"It will be a tough game for us away at Raith, but it is one we are looking forward to.
"We were disappointed that the Cowdenbeath game was off last Saturday as we wanted to go out and get a result for Archie and Scott.
"We will be raring to go for Saturday and hopefully we can get the three points we are looking for.
"Archie is a great leader at the club and he has been a great player for Thistle for many years.
"If we can get a couple of good wins then hopefully he can keep it.
"He has got the respect of the whole squad so I am sure he will do a good job. We are all behind him."
Bannigan and Firhill team-mate Stephen O'Donnell have left their title challenge behind this week after being named in Billy Stark's Scotland Under-21 squad for a friendly with Greece this afternoon.
It is the first time the pair have been called up for national service and the midfielder admits former boss McNamara had a big part to play.
Bannigan said: "It has been a good experience so far, the manager and the all boys have been great with me.
"I trained with them on Monday morning and it went well. I can't wait for the game and hopefully I can get on.
"Obviously I am disappointed to see Jackie leave, he was great with me while he was there.
"It came as a shock to us all and we are disappointed to see him go.
"It is one of those things that happens in football and we have got to move on because we still have a lot to play for this season.
"Jackie played a big part in me getting into the Scotland squad.
"He played me and I have got the recognition at international level by playing well for Thistle.
"He had us playing good football and people were taking notice of us this season.
"A big part of it is down to Jackie, but I have worked hard this year and I am delighted with how things are going.
"I am the best I have ever been, but I know I have still got a long way to go and a lot to learn."
Bannigan's cap call is recognition for his stunning Thistle form this season and he is relishing the chance to star on the international stage.
He said: "I'll just come in and play the way I usually do. I won't try anything different.
"Hopefully I get a bit of game-time today so I can show what I can do.
"I don't know much about the opposition yet but it's something I'll just have to adapt to.
"I've not really played any European football so this will be my first taste of it.
"If you want to be the best in football, you have to play against different kinds of players. I'm sure we will do fine."