Kilmarnock come calling on Sunday, before the Easter Road side play host to city rivals Hearts in the New Year Edinburgh derby.
Butcher has been delighted with the support of the Hibs faithful since he replaced Pat Fenlon at the helm last month.
And he believes the fans can make all the difference as he aims to end the festive period on a high with back-to-back wins in their next two matches.
Butcher said: "To the fans, just keep on doing what you are doing.
"Get behind the boys. The boys are trying in every game.
"They're working their socks off, playing for the jersey and doing everything they possibly can.
"Everyone's confidence is high and we can't wait for these two games to start.
"From the fans' point of view, just keep backing us because we're trying to deliver.
"We know that we are going to score more goals, we are going to get goals at home and we are going to win."
Butcher says the mood in the camp is positive following a Boxing Day win at Ross County, a side they also dumped out of the William Hill Scottish Cup a few weeks ago.
He added: "We've got a fantastic spirit in the squad and it's getting better day by day, game by game.
"We want that to improve because we've got two really exciting matches to look forward to to finish off the festive period."
The Rugby Park side take on Hibernian on Sunday, just days after a morale-boosting 4-0 hammering of Hearts at Tynecastle on Boxing Day.
The victory allowed Allan Johnston's outfit to move to within just four points of St Johnstone in sixth place and only three short of their Easter Road opponents.
And Johnston, who netted a magnificent second for Kilmarnock against Hearts and played a part in the double that took Boyd's tally for the season to 11, insists belief is on the up following three wins from their last four outings.
The 19-year-old winger said: "Sometimes we have struggled to kill teams off but, as you saw against Hearts, it looks like we're maybe getting to grips with that.
"We got two up and scored more, kept creating chances. With someone like Kris Boyd in the team, goals should never be a problem.
"Everybody knows how good he is, a guy of his quality. The goals he scores, it's frightening.
"You know that, if you put the ball into the box, there's a good chance he'll score. He bagged two against Hearts and could have had five.
"If you keep creating chances, he will take them.
"It's great looking at the table now, because we're looking up instead of down. Our aim is to catch the teams in front of us.
"That means going to Hibs and winning. We know it will be a hard game at Easter Road but, if we keep doing the same things we did at Tynecastle, we know we can go there and win."