The Trotters centre-half made the breakthrough at senior international level when he replaced the injured Michael Dawson during Friday night's 4-0 win over Bulgaria at Wembley.
He was the first Trotters player to play for England since striker Michael Ricketts nearly eight years ago.
Cahill had been in contention for a World Cup squad spot until a blood clot in his left arm in February hindered those hopes.
But he gave a competent performance alongside Phil Jagielka after Dawson suffered a twisted knee and ankle when falling awkwardly.
And the ex-Aston Villa player is confident he will not let head coach Fabio Capello down if handed the chance against the Swiss.
Cahill said: "It wasn't ideal to come on in those circumstances because, when you see a team-mate on the floor looking in pain like Michael, it takes the edge off it a little bit.
"Although I was happy to be playing and extremely proud to represent my country, when you come back in the changing room and see him injured on the bed, it does take a bit of shine off it.
"That aside, I really enjoyed it. I've been in and around the squad for eight games or so now, just keeping my head down and waiting for a chance to come on and show what I can do.
"I was so hungry to get on there and I enjoyed it.
"It is strange coming on as a sub. You have to pick up the pace of the game straight away.
"With it being my debut, it was something I hadn't done yet, coming on at Wembley and playing, so that was strange as well."
Cahill admitted: "Coming back from that injury (blood clot) makes you appreciate things a lot more and I came on the pitch with a smile on my face.
"You never want to be injured. You just want to be out there playing football. You can't do anything when injured so, touch wood, I can kick on in my career."
As regards Tuesday's possible start, Cahill said: "Listen, from being a little lad, you strive to play for your country and be where you are now.
"Yes, why not? I am ready for it, definitely, if called upon. It is the manager's decision.
"There are good centre-backs in the squad but, if called upon, I'll be more than happy to go out and play, more than proud."
Cahill, 24, added: "I think the opportunity is there because I've got maybe a bit of age on my side and I can learn from the more experienced boys and they can show me the ropes.
"I've got my debut out of the way, which is a big thing. You come in the squad thinking 'when is the chance going to come'. You just want to make that first step and debut.
"That has been done, I can learn off the boys in front of me, top-quality players, and hopefully be part of the England set-up for a long time to come."
Sheffield born Cahill's hero as a youngster was former England defender Des Walker.
He said: "Being a Sheffield lad, I watched quite a few games there and he was playing centre-back for Wednesday and England at that time.
"I used to watch him quite a bit, a top player."
Source: Team Talk
Source: Team Talk