Killie's 3-3 home draw with bottom side Gretna last Saturday was their first point in six games but they were without Frazer Wright, Simon Ford and Eric Skora who were all ruled out with hamstring injuries.
Grant Murray and Allan Johnston missed the game with knee problems, and Rhian Dodds was another absentee due to a hip injury.
Jefferies, having agreed terms with Inverness wide-man Alan Morgan who will join the club on January 1, said his best Christmas present would be an empty treatment table.
He said: "I don't know what my wife and kid will get me for Christmas but, from a football point of view, I would like to get all my injured players back.
"It's been difficult with losing players like Gordon Greer, Peter Leven and Stevie Naismith and we have had a lot of injuries.
"It's not been a great season for us in terms of getting a break. When you are down, things do go against you.
"It's always been a challenge for us to get into the top six in the last couple of seasons and that is the target.
"There is more than half a season to go and they say that breaks always even themselves out. So, if we get our players back, hopefully we can put in that challenge."
Jefferies welcomed the forthcoming addition to his injury-ravaged squad but hopes at least another two players will arrive in the new year.
He said: "I'd like to thank Craig Brewster for giving me a courtesy call to inform me that Alan was out of contract and looking for a move.
"I watched Alan when he was at Blackburn and I thought he did reasonably well when he got the opportunity at Inverness.
"We are short of left-sided players and we feel that he can be a good addition to our squad.
"I won't be buying players or even increasing the wage bill.
"If anyone comes in, there will need to be players going out.
"We hope to bring another two in and we are down the road with one of them."