Mr Swinney stressed that Holyrood had the chance to ensure that it supported the budget, which will provide funding for free school meals, childcare, to mitigate the bedroom tax and to support small businesses.
He was speaking ahead of the stage one debate for the Budget Bill that covers the next financial year.
Mr Swinney said: "Within our limited powers we are doing everything possible to tackle the effects of Westminster's cuts to the Scottish budget on our economy and their relentless austerity agenda.
"This budget contains proposals that will help Scotland's children, tackle poverty, increase the opportunities for parents to work and protect some of our most vulnerable people from the impact of welfare reform.
"They are proposals that the whole of Parliament should be able to endorse."
Scottish Conservative finance spokesman Gavin Brown MSP said: "The SNP needs to back up its rhetoric with action.
"We need to see a budget that is going to put the economy at the forefront of political decision making.
Scottish Liberal Democrat leader Willie Rennie said: "I wrote to John Swinney on the 19th December to set out the reasonable proposals of the Scottish Liberal Democrats for changes to his budget."
Labour has pledged to keep up the pressure over housing and housing benefit-related issues.