Their pursuit of glory in the SPL, Scottish Cup and Uefa Cup to add to last Sunday's CIS Insurance Cup final win looks to be taking its toll on Rangers, who had to come from behind to force a 1-1 draw against Partick Thistle in their quarter-final tie at Ibrox.
With no free midweek dates available because of Scotland's friendly against Croatia next Wednesday, then Rangers' two-legged Uefa Cup quarter-final against Sporting Lisbon on 3 and 10 April, the Firhill replay against the mid-table First Division side is likely to go ahead on 13 April, which is the scheduled slot for the semi-final against St Johnstone.
Ally McCoist, Rangers' assistant manager, admitted that the fixtures backlog is causing increasing concern.
"A replay was the last thing we wanted," he said. "It is another fixture, which we could do without, but we just have to get on with it. I've got no idea when the replay will be, but we will have to be ready for it when it comes around."
McCoist expressed his disappointment at the poverty of Rangers' performance on a night when they made six changes to the starting line-up which had beaten Dundee United after extra time and penalties at Hampden.
"I thought we would be a lot better than that," he said. "We were really poor tonight. I'm delighted we are still in the cup, although as badly as we played, I don't think we deserved to lose the game.
"Our use of the ball in the final third of the pitch just wasn't good enough. With the changes we made, I expected it might take us longer to get going, but we never really got started at all. To win anything in modern football, you need a squad of more than 20 players who can come in and contribute.
"I'm not sure fatigue was the reason for our performance. It was more about ability. The lads have been brilliant recently and have deservedly received a lot of praise, but they deserve criticism when they play as they did tonight."
Damon Gray, the 19-year-old English striker on loan from Hibs, gave Thistle a 67th-minute lead but they were able to hold it for less than two minutes before Kris Boyd scrambled home his 21st goal of the season.
"If we had kept the lead for another five minutes, we could have won the game," said Thistle manager Ian McCall. "There was an element of fortune in Rangers' goal, but Kris Boyd scores fortunate goals and that's the sign of a great striker.
"I thought our team showed real balls to take possession and pass it the way they did tonight, rather than just kick it away. We have seen a lot of shocks in the cups on both sides of the border this season and, who knows, there might be another one."
It remains to be seen if goalscorer Gray will be in the Thistle line-up for the replay. His loan period expires this weekend and he is due to return to Hibs on Monday.
"I'll speak to Hibs and I would like to stay for the replay," said Gray. "I want to play for Hibs' first team, but if that's not happening then I'd be happy to stay with Thistle until the end of the season."
Rangers captain Barry Ferguson missed last night's match, but is expected to return for the SPL fixture against Hibs on Saturday. The midfielder saw a specialist on Tuesday but will not require surgery on a persistent ankle injury until the end of the season.