In a speech in London which may irritate some on the right wing of the Conservative-led coalition, Deputy Prime Minister Nick Clegg will warn that "household budgets are approaching a state of emergency, and the government needs a rapid response".
Finance minister George Osborne is expected to announce an increase in the personal allowance for income tax in his March budget, but there is no indication yet whether he will meet Clegg's challenge.
Britain's economy contracted in the last three months of 2011 and, with unemployment rising and wages stagnant, the government is facing greater pressure to soften its austerity plan of big spending cuts and tax rises.
Clegg's push for a smaller tax burden on the lowest paid in the economy, however, would be a fiscally-neutral move.
"I want to help hard-pressed and hardworking families. If that means asking more from those at the top, so be it," Clegg will say, according to extracts of his speech released in advance by his office.
The Conservative-led coalition has already committed to raising the threshold at which employees start paying tax to 10,000 pounds by 2015. That is a crucial pledge for the Liberal Democrats, who have had to abandon several policies since signing up to a coalition in 2010 which has damaged their popularity.
The personal allowance for income tax will rise in April to 8,105 pounds from the current 7,475 pounds for the year 2012/13.
"I want the coalition to go further and faster in delivering the full 10,000 pounds allowance because the pressure on family finances is reaching boiling point," Clegg will say.
A source close to Clegg said the Liberal Democrat leader and party colleague Danny Alexander finance minister George Osborne's number two at the Treasury will be pressing the case within government ahead of the March 21 annual budget.