The Job Centre could be shut down for two days at the end of the month over a pay dispute.
Swindon members of the Public and Commercial Services Union are voting on strike action after receiving what they consider to be a derisory pay rise.
Ballot papers are being sent to members this week and the result will be announced shortly after voting ends on January 20.
Staff and management disagree about what the pay settlement, introduced in December, means for workers at job centres across the country.
The PCS union said it amounted to an average rise of only 2.6 per cent below the 3.2 per cent inflation level.
But the Department of Work and Pensions has said the majority of staff had been given five per cent.
Ian Robertson, union representative at the Swindon Job Centre in Clarence Street, said: "It is well below inflation and well below what we would have expected."
Mr Robertson said the strikes, which would take place on January 29 and 30, could be avoided if the Department of Work and Pensions was willing to come up with a better offer.
"We are not a militant union and would prefer not to take this action," he said.
But he warned if members voted for industrial action the two-day stoppage might not be the last.
A spokeswoman for the Department of Work and Pensions said its offer had been a substantial one.
"Over 84,000 staff, most of them working at the front line, have been offered a rise of five per cent or more," said the spokeswoman.
"Given the scale of this pay offer any industrial action would be wholly inappropriate."
Employees at the social security office in Princess Street are also being balloted.
Job Centre managers and union representatives both said they expected emergency benefits payments would still be made in the event of strikes going ahead.
Andy Tate
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article