Local authority bosses aim to protect vulnerable people with carers, social workers, refuse collectors, librarians and street cleaners among hundreds of workers walking out.
Unions say members are underpaid, but Mr Browne believes industrial action will only cause inconvenience as the UK battles to recover from recession and government debt.
Mr Browne added: “People in the public and private sector have had to contribute to getting our economy back on track.
“We’re starting to see some progress with the economy growing and unemployment falling.
“It would be a terrible mistake to give up now and go back to dangerous levels of borrowing.
“Nobody is claiming that times are easy, but I don’t think a strike will alter the fundamental economic reality.
“It will only cause inconvenience for hard-pressed parents and other people who rely on our public service and fund them through their taxes.”
UNISON members taking the day off work are manning a stall in High Street, Taunton, and collecting donations for Taunton Foodbank.
Kris Ross-Osborne, the union’s Somerset assistant branch secretary, claimed five years of pay freezes and below inflation increases have hit local government workers.
He added: “We believe public services are important and worth fighting for.
“We’re clear that if we want to preserve them in the future, then the staff that provide them deserve fair pay for the work they do.
UNITE representative at County Hall Nigel Behan said local government is “a low wage employer” and is demanding a £1 an hour increase.
He said: “By taking industrial action, you’re saying you’re fed up with receiving real pay cuts and are prepared to fight to get a better pay deal.”
A Taunton and West Somerset Trades Council spokeswoman said further cuts planned at County Hall would result in “huge further job losses, continuing salary cuts and major losses of service provision”.
She added: “Striking public sector workers are going to use the day to engage with the public, drawing attention to the impact of growing poverty in Taunton.”
A Local Government Association spokesman said it has offered to increase most employees’ pay by 1%, with the lowest paid offered over 4%.
He added: “This strike won’t change the pay offer we’ve made, but it will mean those who take part lose a day's pay.”
Firefighters and members of the NUT teachers union are also on strike tomorrow.