During conference season, the Conservatives said the bid to set a £10,000 personal allowance target was a "Tory tax cut" and now their party HQ is said to be drawing up plans to make a further push to £12,500 a key election pledge in its 2015 manifesto, thus taking out of tax all those on the minimum wage.
The move is part of David Cameron's fightback on the issue Labour has dubbed the "cost of living crisis".
One senior Tory figure said: "We will have to see if the numbers add up nearer to the election but, of course, we are keen to do it." Meantime, a Cabinet member claimed the policy would be pushed through as it would let the party answer Ed Miliband's populist interventions on the energy price freeze and the 10p tax rate.
But Mr Alexander, on the LibDem Voice website, claimed the push to £12,500 had been his party's policy since spring last year. "It is the Liberal Democrats who are shaping the future of the British tax system," he said.
The Chief Secretary to the Treasury said party leader, Nick Clegg, set out in April 2009 plans for a £10,000 personal allowance. He said during TV debates before the 2010 election, the Tory leader had told Mr Clegg: "I would love to take everyone out of their first £10,000 of income tax Nick...(but) we cannot afford it."
He added: "This is the Liberal Democrats policy and everybody knows it."