This seems to be a misunderstanding of the situation. Currently the ECB is propping up the banking system to the tune of 130Bn. Unchecked that could rise to 250Bn and more if there was a retail run on the banks.
The government are being allowed a 40 bn fund to capitalise the banks and try and encourage bondholders back. If it doesn't work it is the ECB who remain on the hook. Ireland is not borrowing to fund the banks rather to capitalise them. So, in summary, yes the .25Tn is possible but it will mostly come from the ECB.