Nick Clegg has urged the government to go "further and faster" in raising the level at which people start paying income tax to £10,000 a year.
The deputy prime minister argued many families were facing a "state of emergency" in their finances and ministers must respond "more rapidly".
The coalition has promised to raise the income tax threshold to £10,000 by the next election, set for 2015.
But Labour said the coalition was to blame for the "squeeze" on families.
In a speech to the Resolution Foundation in London, Mr Clegg attempted to set out a distinctive Liberal Democrat fiscal position by highlighting differences with the party's Conservative coalition partners.
His remarks follow official figures showing the economy shrank by 0.2% in the final quarter of 2011 and ahead of the Budget on 21 March, increasing speculation that changes to tax thresholds could be announced.
Mr Clegg said the "biggest question" facing the country was how the tax burden on people was shared.
While the coalition had "called time on the unfair and out of whack tax system", he said Lib Dem priorities were different from those on the right in politics who placed "less of an emphasis on using the tax system to tackle inequality".
At the last election, the Lib Dems pledged to raise the income tax threshold to £10,000 a year and the coalition agreed to implement this policy over the course of this Parliament.
The income tax threshold was raised by £1,000 to £7,475 in the 2010 Budget, and the government plans to increase it further to £8,105 this year.
Mr Clegg said he was proud of these measures, as "cutting income tax is one of the most direct tools we have to ease the burden on low and middle earners".
And he added: "Today I want to make clear that I want the coalition to go further and faster in delivering the full £10,000 allowance, because bluntly the pressure on family finances is reaching boiling point.
"Compared to those at the top, these families have seen their earnings in relative decline for a decade. That has got worse since 2008, with lower real wages and fewer hours at work."
Mr Clegg said the pledge - which would cost an estimated £9bn - had to be fully funded, stressing "we need to find the money and that won't be easy of course".
But he argued the UK could not afford not to address inequalities in the current system.
He also said he would "stick to his guns" in arguing the case for a "mansion" tax on property - aimed at homes worth more than £2m - as part of his plans to tackle "serious, unearned" wealth.
Mr Clegg discussed his tax objectives with Chancellor George Osborne on Wednesday and Prime Minister David Cameron on Tuesday.
But the BBC News Channel's Chief Political Correspondent Norman Smith said although Mr Clegg was pushing hard on the issue none of his demands had been "signed off" by No 10.
Ahead of the speech, Mr Clegg told BBC One's Breakfast: "I can't tell you exactly what's going to be in the Budget, because it hasn't been decided yet, but this is very much what I think should be in it."
But the plans were criticised by Conservative MP David Ruffley, a member of the Treasury select committee, who said there were "better ways" right now to boost economic confidence - such as cutting workers' national insurance contributions.
"In case Nick Clegg had not noticed, the deficit is not falling as quickly as we would like because growth is more sluggish than we would like," he told the BBC News Channel.
"It is perfectly clear he is doing this for political reasons and is trying to get a few brownie points. In good time, we will get to the £10,000 tax free slice. It is all good stuff but there are priorities here."
Mr Ruffley warned Mr Clegg against "pushing Conservative backbenchers around" on tax, particularly over issues like property taxes and tax relief on pension contributions.
"You should not play politics with the economy which is what I fear Nick Clegg is doing. I think he is trying to bounce the chancellor which is not a wise thing to do."
Labour leader Ed Miliband said it was the coalition government which had put up VAT, cut tax credits and "allowed energy and train companies to rip people off on their bills".
"Finally Nick Clegg has woken up to the squeezing of people on middle incomes," he said. "But the problem is who squeezed the middle? It is this government.
"I don't think people are going to trust Nick Clegg or this government to help the squeezed middle."