The Government will today be urged to ask the EU for a one-off change to European treaties.
TDs from the Technical Group want a one-off exemption so that the Central Bank can write off €28bn of Ireland's debts.
The TDs say Irish citizens should not have to foot the bill for the costs of liquidating the former Anglo Irish Bank.
Nineteen opposition TDs have tabled a motion in the Dáil calling on the Government to seek a one-off exemption to the EU rules on so-called "monetary financing".
Those rules mean the ECB cannot simply lend money directly to a Government to help it pay its bills.
The TDs say Ireland' is a special case and want permission for the Central Bank of Ireland to destroy €28bn of debts run up in the last two years.
That includes the €25bn of bonds issued when IBRC was liquidated earlier this year, and €3bn borrowed last year to cover the repayment of the promissory notes.
The Government is certain to vote against the plan - but even if it were passed, Ireland would still face the difficult task of convincing every other EU member states to agree with the idea.