David Cameron has ruled out "significant" tax cuts while the Government is cutting spending to reduce the deficit.
The Prime Minister said he wanted to offer people "relief", but suggested that would only be possible "at the end of this hard road".
His comments came in an interview with The Sunday Telegraph ahead of the March 23 Budget.
Chancellor George Osborne is facing calls to reduce the burden on hard-pressed voters as inflation spirals. Tory Mayor of London Boris Johnson urged him last month to set out "a clear direction of travel" on how taxes could be reduced.
But Mr Cameron insisted there was no "Plan B" on the coalition's deficit-reduction strategy and said tax cuts would only undo the work of painful curbs in public spending.
"I would love to see tax reductions. I'm a tax-cutting Tory and I believe in tax cuts, but when you're borrowing 11% of your GDP, it's not possible to make significant net tax cuts. It just isn't," he said.
"It's no good saying we're going to deal with the deficit by cutting spending, but then we're going to make things worse again by cutting taxes. I'm afraid it doesn't add up."
Later in the interview, he added: "Do I want to see, at the end of this hard road, relief and lower taxes for hard-working people? Yes I do."
It was also reported today that Mr Osborne was considering a new tax levy on wealthy "non-doms" which could be announced as early as the Budget.
The move would help fund the coalition's commitment to raise the income tax threshold to £10,000.
Former prime minister Gordon Brown introduced a £30,000 annual charge on non-doms - people who cite foreign connections to avoid tax on their overseas earnings - who have lived in Britain for seven years.
According to The Sunday Times, Treasury documents show that four out of five of the UK's 120,000 non-doms do not pay the levy as they leave within seven years. It raises only £160 million a year.
Options to increase income from non-doms would be to impose the levy earlier than after seven years or even to impose a tax on overseas earnings after that period.
The coalition agreement promised a review of taxation paid by non-doms.
Lib Dems are pushing for the issue to be tackled swiftly so that tax revenues from any change can be maximised during the austerity years.
Lord Oakeshott, a Lib Dem Treasury spokesman, said: "Non-dom status is the biggest tax loophole in Britain.
"The £30,000 non-dom poll tax is a joke - it's only the tip they give the waitress after drinks in the directors' box at Chelsea or Manchester City.
"We must redouble our efforts to make non-doms pay their fair share."
From April, 500,000 people are expected to stop paying income tax altogether as the income tax threshold is raised to £7,475, on the way to £10,000.
However, an economic think-tank has calculated that a simultaneous drop in the higher rate threshold will put an extra 750,000 into the 40% income tax bracket.
Energy and Climate Change Secretary Chris Huhne said the Government needed to clamp down on those who avoid paying tax.
He told Sky's Dermot Murnaghan the Coalition was taking action on bankers' bonuses but added it would take time. "Rome wasn't built in a day", he said.
"On the tax avoidance point, that's absolutely key. I think we need to get tougher and rougher with some of the off-shore tax havens and there has been progress on that."
He added: "I am not against whether they are footballers or bankers, people who have particularly high skills and talents being paid... whatever you can get in the market place.
"But the key point is, is the pay actually there for real talent or is it there frankly because the structure is not delivering? I think with the bankers we have to see that the incentives actually align with their performance."