The Jags are currently two points adrift of Allan Moore's side at the top of the table heading into this weekend's fixtures.
Thistle should have completed their two games in hand over the Ton by the time they travel to Glasgow on April 10.
The Firhill side host Livingston tomorrow while Morton are at home to Cowdenbeath and interim Jags boss Archibald expects the race for promotion to go right down to the wire.
He said: "Quite possibly it might take eight or nine wins to win the title, you just don't know what is round the corner and what Morton will do.
"Every team is fighting for points and there will be no easy games between now and the end of the season.
"I think it will go right down to the wire.
"We've got a massive game against them in a couple of weeks which will have a big say, so it's vital that we win all the games leading up to that one."
Despite facing a hectic fixture schedule as they chase a historic league and cup double this season, Thistle are well placed to pounce in the promotion push as the finishing line draws closer.
They made it a six-game run unbeaten under Archibald last week with victory over Hamilton and recorded a fifth consecutive clean sheet.
Livi travel to Firhill under the guidance of interim boss Richie Burke and Archibald knows the Lions pose a significant threat.
He said: "They are in a very similar situation to ourselves with myself and Richie being interim managers.
"If the players like the training and the way they play they will be desperate, like our lads, to put in a good performance.
"A few of them will be out of contract in the summer so everyone will be playing for something."
Thistle will be without the services of midfielder Stuart Bannigan tomorrow after he picked up his sixth booking of the season in the recent 4-0 win over Dunfermline at East End Park.
The Jags star will again join up with the Scotland Under-21 squad for their Euro Championship Qualifier with Luxembourg on Monday night and Archibald is delighted to see the Partick protege earning international recognition.
He said: "Stuart is a massive loss. He has been one of our best players – if not the best – this season.
"It is great for his confidence to go away with Scotland. He is a great lad who has been brilliant for us and thoroughly deserves his call-up."