Unite, the union representing nearly 150 bus engineers, say the transport giants "wrecked" the talks after making a two-year offer of a 1.2% rise.
The 1.2% annual rise for 2014/2015 was initially rejected by 145 of the total 148 workers less than 24 hours before the new bid was made.
Union officials and workers were left dumbfounded when the firm's managing director Fiona Kerr said the firm would not be prepared to move further than the two-year offer.
The discussions at Acas appear to be at a standstill, with workers balloting for strike action on Wednesday.
After the vote concludes on July 9, seven days notice must be given prior to any strike, which has to be taken within 28 days of the ballot. It is thought the transport workers would vote in favour of the strike to be held during the Games.
Unite's regional industrial officer Eddie Duffy said: "First Group management wrecked conciliation efforts and it's difficult to see how we are going to resolve this dispute if the employer is not prepared to listen to its workers and to help them combat the rising costs of living.
"Unfortunately, industrial action during the Commonwealth Games is a now very real possibility unless First Group gets its act together fast and negotiates seriously."
Ms Kerr questioned Unite's ability to represent its members after the initial offer was rejected, and said it was "hugely disappointing that Unite the Union continue to threaten the success of the Commonwealth Games by attempting to use such an important event as leverage in pay discussions".
She also urged the union to ballot its members on the new offer, not the previous one, "so that we can properly listen to their views".