The Irish Republic is set to unveil more details of a severe austerity budget later.
Finance Minister Brian Lenihan is planning an initial 6bn euros (£5bn; $8bn) of cost cuts in the toughest budget in the country's history.
It is part of a deal to secure an 85bn-euro bail-out from the European Union and International Monetary Fund.
Despite the Fianna Fail/Green party coalition's slim majority, the budget is expected to be passed.
If the budget is cleared by parliament, it will trigger the first tranche of bail-out funds from the EU and IMF.
The scale of cuts and the government's handling of the crisis have been heavily criticised and a demonstration is expected outside the Irish Parliament after the budget.
Earlier, police arrested a protester who arrived with a crane covered in slogans attacking the banks and politicians.
The government previously announced cuts under a four-year National Recovery Plan unveiled two weeks ago.
Dublin is looking to save about 15bn euros over the period as it struggles to balance the books, with the biggest cuts of the plan coming this year - between 2010/11.
The Irish Republic's generous welfare budget is a prime target for the axe.
Child benefit is being slashed, and social welfare spending - state pensions excluded - is being cut by 5%.
Thousands of public sector jobs will go. Civil service pay freezes will be imposed, and reform of the tax system will bring thousands of Irish people into the tax net. The minimum wage will be lowered.
Mr Cowen says the cuts are necessary because the Irish Republic was living way beyond its means.
Surging bond yields - the interest rates Dublin pays to borrow money - forced the government to ask for a bail-out on 28 November, as the Republic could no longer afford to raise money in the financial markets.
Mr Cowen, with his poll rating at a record low, needs to push the budget through to avoid having to call a snap election.
Failure to do so could plunge the Republic into a deeper crisis, one that could help spread contagion throughout the heavily-indebted eurozone.
Mr Cowen's government only has a majority in the Dail, or lower house of parliament, thanks the support of two independent MPs.
One of these MPs, Michael Lowry, pledged his support for the budget on Monday evening.
"This budget is going to be harsh. It's going to be extremely difficult," Mr Lowry told the BBC.
"People will be angry," he said, "but if we are to survive into the future and if we are to restore our economy, these difficult and harsh decisions have to be made."
According to reports, the other independent MP, Jackie Healy-Rae is expected to follow Mr Lowry's lead.
And it is not clear if all opposition MPs will oppose the budget. There has been talk of some MPs abstaining from the vote, strengthening Mr Cowen's hand.
Opposition parties have published their own budget proposals ahead of a general election next year.
But with stringent EU/IMF fiscal targets to hit, most politicians accept that there will be little scope to deviate greatly from today's plans.
But it is not essential that all parts of the budget are cleared on Tuesday.
The vote will be conducted via four separate ballots, and the budget must be passed within four months of Mr Lenihan presenting it to parliament.