Independent TDs Michael Lowry and Jackie Healy-Rae have pledged their support for the Finance Bill following discussions with the Taoiseach this morning.
In a statement after the meeting, Mr Lowry said he had been given assurances that an amendment to deal with a supertax on bankers' bonuses would be brought forward.
He also blamed the controversy over which way he would vote on the limited one-week timeframe Fine Gael and Labour had forced on the Bill.
"It is appalling and unacceptable that the proposed taxation measures on bankers' bonuses were not to be dealt with because of the time restriction placed by Labour and Fine Gael on the passage of the Bill," Mr Lowry said.
"The minister has agreed to my request to introduce an amendment to deal with this issue."
Mr Lowry said the minority Government secured his support after he was given assurances on tax relief on student fees and tax return issues for farmers.
Mr Healy-Rae also attended the meeting.