But Nationalists are under pressure to explain their own “skeletons in the closet” in the battle for the local town hall which is gearing up to be one of the most bitterly contested campaigns in the coming weeks.
The ruling Labour administration points to the controversy surrounding Nationalist councillor Lynda Kenna who quit as head of the local fire board in 2008 after being taken to court for a £2,000 debt.
Joyce resigned from the Labour Party last month after assaulting fellow politicians in a House of Commons bar brawl, while subsequent claims about his relationship with Meg Lauder, then aged 17, also proved damaging.
Falkirk’s SNP group leader David Alexander said: “It’s very clear that Labour in the area are demoralised and downhearted.”
He pointed to the role of Michael Matheson, the local MSP and SNP public health minister, adding: “The majority of people who will swing between the SNP and Labour are the ones who are drawing comparisons with the type of responsible representation that Michael Matheson brings.”
Mr Alexander added: “The Eric Joyce issue is playing out on the doors. It will impact on the outcome on 3 May.”
But Labour points to the Nationalists’ own troubles including Ms Kenna’s departure from the local fire board. She cited “family reasons” at the time, but that came after she was ordered at court to repay £2,000 she borrowed from a constituent.
Labour’s council leader in Falkirk, Craig Martin, said it raised questions over why the SNP allowed her to stand again.
“David Alexander must have know about this,” he said. “That would never happened in the Labour party. The Labour party selection process is absolutely clear. If you have a criminal record, or any type of incident, that should be brought forward and discussed.”
He added: “The skeletons in the SNP closet are coming out fast and furious now.”
Labour currently runs the administration in coalition with the Tories and independents, having seized power in 2007. The SNP had been in control since 2001 in coalition with Independents.
Mr Martin says in recent years the council has lost almost 10 per cent of its budget in real terms, but no schools or sports centres have been closed.
Falkirk has seen record low levels in school leavers being unable to find work, despite the economic downturn. “We’ve got an excellent story to tell over the last five years,” he said. “Our job is to try and keep the Nationalists out of power in Falkirk and we’ll be doing that as much as we can.”
The SNP points to new charges for elderly and disabled people which have been introduced as a “poll tax” meaning everyone pays the same.
“We can understand an argument that would say we want the rich pensioners to pay, but we will protect the poor – no-one has been protected in Falkirk,” Mr Alexander said.
The rising cost of healthy school meals have also been a concern for the SNP.
“There’s definitely a swing in our direction and its very similar to last year,” Mr Alexander added.
It is unlikely under the the single transferable vote (STV) system that any party will gain an outright majority in Falkirk, but the Nationalists believe they will emerge the biggest party.
They point to the fact that Labour have put up 16 candidates for 32 seats, while the SNP are standing 18 candidates.
“We’re the only party that is trying to win outright,” Mr Alexander added.