The two opposition parties say it is necessary to up taxes to provide almost £500 million of additional funding for education.
The budget for 2016-17 marks the first time Holyrood ministers have been required to play a part in determining income tax rates in Scotland.
With the Scottish rate of income tax due to come into effect from April 6, the Scottish Deputy First Minister has pledged to keep payments in line with the rest of the UK.
In addition Mr Swinney said his draft budget - which will be voted on for the first time by MSPs today - would give up to 51,400 low paid workers a pay rise, by uprating the living wage and extending this to social care workers as part of the local government settlement.
But the Deputy First Minister is currently locked in a stand-off with councils over their funding, with the local authority body Cosla arguing authorities face a ‘’totally unacceptable’’ £350 million of cuts.
Scottish Labour leader Kezia Dugdale has tabled an amendment to the the budget, calling for the Scottish rate of income tax to be set at 11p, a penny more than the rate proposed by the SNP administration.
Labour argues this cash would help avoid cuts to schools and other vital local public services, with Ms Dugdale insisting the new tax raising powers must “not lie unused on the shelf’’.
She has written to First Minister Nicola Sturgeon, telling her: “By supporting my plans for real terms protection for education in the next Parliament and for a Scottish rate of income tax of 11p we can ensure there would be no cuts to the budgets for our schools and vital public services.
“I am willing to work with you on this issue and propose an urgent meeting between the two of us to discuss this in person before the end of the budget process.”
Labour’s plans for a 1p rise in income tax were unveiled days after the Scottish Liberal Democrats proposed increasing the levy to help fund education.
Holyrood leader Willie Rennie said: “As it stands, this SNP budget will deliver the harshest cuts to education in a decade and responsibility for those will lie squarely on the shoulders of John Swinney and his SNP colleagues. But the Deputy First Minister can be assured that Liberal Democrats stand for a transformational investment in education with a penny for education.
“John Swinney has spent all of his political life calling for increased powers for the Scottish Parliament. Well now he has them. Now he could use them. But instead he’s decided to undercut George Osborne on tax.
“Instead of talking left and walking right, the SNP should support Liberal Democrat calls for a penny for education. The £475 million that would be raised by adding one penny onto each tax rate would bring our education system back up the international standing.”
But speaking ahead of this afternoon’s debate, Mr Swinney said: “I will not penalise those on low incomes, and I certainly won’t increase their tax bill. Instead this budget will see up to 51,400 lower paid workers receive an increase in pay.”
He added: “Our budget will see an additional £250 million invested in social care, around £13 billion for health, it will freeze council tax for a ninth consecutive year, protect police budgets, invest £690 million in housing, allocate over £1 billion for higher education, and protect the pupil-teacher ratio, helping improve attainment.
“Our budget will equip the country for the future and lay the foundations for the reforms that will define the next parliament - reforms that will reshape our health and social care services, deliver a step change in educational attainment, deliver a fairer system of local taxation and use new powers over tax and welfare in a way that supports our central purpose.
“The current financial landscape presents us with a challenge and a choice: Scotland can accept these UK Government cuts or we can rise to the challenge and chose a Scottish alternative to austerity. We choose to rise to the challenge. This is the Scottish alternative.”