A number of senior players are still waiting for their wages, which were due on Wednesday, after experiencing a 19-day delay on their October payment.
The instability intensified yesterday when owner Vladimir Romanov claimed he had instigated attempts to sell the club after becoming disillusioned with football.
With the club’s debts standing at around £35million, players are likely to be offloaded in January and no date has been specified for their latest payment, which the club say was delayed because of a £1million tax bill.
But Sergio, who begins a five-match touchline ban against United, insists his players will play for the jersey.
“The team is very well,” the Portuguese manager told Hearts TV. “We have lots of problems, like everyone knows, but we have a group that knows to stick together and fight for Hearts’ interests.
“We are going to be strong, we are going to be together and we are going to fight for three points against Dundee United.
“It’s not an ideal situation, some things that we are living here, but we still believe that everybody is working to fix all the problems and to let the professionals think just about football.”
Sergio was banned by the Scottish Football Association after remonstrating angrily with referee Alan Muir after being sent to the stand during a 1-0 defeat by Kilmarnock last month.
Sergio, who revealed his only other dismissal from the touchline came when he managed Sporting Lisbon last season, admitted his reaction was wrong.
But he remains frustrated over his sending-off and said he would have to curb his comments in future, although the fact that the club are refusing to speak to the outside media should help him in that respect.
“I’m not proud of my reaction after I was sent off,” Sergio said. “I can’t be proud of that. I don’t want to give that example to anybody. But I just want to remind that I lost my temper because I was sent off because I hit my dugout with my hand. I see all day pictures in the newspapers of other managers doing worse than that. But I have to learn. Maybe I shouldn’t say anything more because maybe I get another suspension.”