Labour is pledging not to raise income tax for those earning less than £80,000 a year as part of an election "personal tax guarantee" for 95% of taxpayers.
The shadow chancellor said those on more than £80,000 would pay "a modest bit more" to fund public services.
Despite local election losses last week, John McDonnell said he believed Labour would win the 8 June election.
The Tories, who have ruled out a VAT rise, say Labour are "going back to type - they want to tax aspiration".
Mr McDonnell told BBC One's Andrew Marr Show that Thursday's local elections had been "disappointing" for Labour and the party's campaigning had to "step up a notch" before the general election.
But he said they would fight "for every vote" and predicted it would be "a young people's election as much as anything".
Asked whether he and party leader Jeremy Corbyn would step down if Labour lose, he said: "We are not contemplating any loss. We are going to win the votes and we are going to win this election."
Labour says low and middle earners would be protected from rises in the overall tax burden in the next Parliament - until 2022 - while the top 5% of earners would pay more to fund public services.
The party is ruling out increases in the standard 20% rate of VAT, personal NI contributions and income tax rates for those earning less than £80,000.
Mr McDonnell said he wanted to offer reassurance to the majority of tax payers, but said the details would be outlined in Labour's manifesto.
Asked whether the party would reinstate the 50% income tax rate on earnings above £150,000 a year - the current rate is 45% - he said Labour was planning to determine the level in the coming week.
But he said there were no plans for a rise in employers' National Insurance contributions or to change those products which are "zero rated" for VAT - with the exception of fees for private schools.
Pressed on whether he was a Marxist, he said: "I believe there's a lot to learn from reading [Das] Kapital, yes, of course it is, and that's been recommended not just by me but many others, mainstream economists as well."
But when it was put to him that Das Kapital predicted capitalism would fail and asked whether he wanted to bring down the system, he said: "I want to transform the system - that's where Marx got it wrong, we know that."
Labour's spending commitments so far include:
- Recruiting 10,000 new police officers
- Giving NHS workers a pay rise of more than 1%
- Reinstating training bursaries for student nurses
- Bringing back the educational maintenance and carers allowances
- Restoring student grants
The majority of these, it says, will be covered by the reversal of cuts to corporation, capital gains and inheritance taxes.
The Conservatives are not expected to confirm their own plans until their manifesto launch later this month.
Analysis by BBC business correspondent Joe Lynam
HMRC figures show that the top 5% of earners pay almost half (47.1%) of all income tax in the UK.
The figure for the top 1% is 27%, with the top 10% paying 59% of all income tax. The poorest half of the country pays only 10% of all tax.
But according to ONS data, the less well-off (the poorest fifth) pay a higher slice of their total income (38%) in tax than the most wealthy (top fifth of earners) in Britain.
Then there's the issue of whether increasing taxes would yield more money for the exchequer.
Paul Johnson from the Institute for Fiscal Studies said that the very wealthy might find new ways to avoid tax - or they might even move away. He said that there was no big pot of gold out there that previous governments had overlooked.
Prime Minister Theresa May has said she has "no plans" to raise other taxes after the election, but has declined to back a 2015 pledge that also ruled out rises in income tax and National Insurance.
Chancellor Philip Hammond has said that "greater flexibility" would be needed in future to pay down the deficit and reduce levels of debt. He abandoned proposals in March's Budget to increase national insurance contributions for the self-employed following a Tory rebellion, with MPs claiming the move breached its 2015 manifesto.
During the coalition years, the focus of Conservative policy was steady increases in the personal tax allowance. The threshold rose to £11,500 last month and is due to increase to £12,000 by 2020.
After winning the 2015 election, the Conservatives also raised the level at which people start paying income tax at 40% - which has now reached £45,000.
'Judge on record'
Conservative Home Secretary Amber Rudd told BBC 5 live's Pienaar's Politics: "Labour did badly in the local elections... and naturally they are going back to type, they want to tax aspiration.
"They are always going to raise taxes. They will start at £80,000, you will blink and they will bring it down again."
Asked why the Conservatives had not repeated their 2015 pledge not to raise taxes, Ms Rudd said: "We don't want to restrict ourselves at the moment. Nobody knows what the future holds.
"What we would ask people to do though, is to judge us on our record. This party reduces taxes and makes sure that the lowest paid come out of tax."
The Lib Dems have pledged to put 1p on income tax to pay for increased health spending.
The party's Treasury spokeswoman Susan Kramer said: "John McDonnell has no credible plan for the future of our economy and no guarantee to employers that they won't be hit with a jobs tax."