New York senators Kirsten Gillibrand and Charles Schumer said this weekend that a vote is likely on whether to begin formal debate on the bill.
The measure would provide up to $7.4 billion in health care and compensation.
Supporters say they are optimistic they can win two Republican votes along with the support of all Democrats. That would be enough votes to break any GOP blocking tactics.
Critics have questioned whether the bill is affordable and does enough to ensure that only people with illnesses related to trade center dust get paid.