The Government needs to sway cross bench senators to pass the legislation in full because Labor is lobbying for the bill to be split.
Next week, the Senate will resume debate on the rest of the Government's business-tax plan, which would reduce the corporate-tax rate from 30 to 25 per cent.
The Government fell two votes short of getting the plan passed in April, and, since then, One Nation senator Pauline Hanson has reneged on an agreement to support it.
Senator Brian Burston, who split from One Nation over the issue and later joined Clive Palmer's new political party, says he will stick to the agreement with Senator Cormann to support the cuts in full.