This page informs us that at 10am today there will be:

a vote on a cloture motion – a motion to end debate on the bill in preparation for passage. If the cloture motion passes, a limited number of germane amendments could still be brought up if agreed upon in advance, but a final vote on the bill would likely be held Wednesday or Thursday. If 40 Senators (normally it would be 41, but Sen. Rockefeller is at home following back surgery) vote against the cloture motion, Senator Frist will have to choose to allow the debate to continue or let the bill die and move on to other business. He is almost certain to choose the latter.

Please contact your senators and let them know what you think: senate.gov

UPDATE: The cloture motion passed. And, from Senate likely to pass bill on aliens:

The Senate is expected to approve as early as today the most significant and wide-ranging immigration reform legislation in two decades.

The bill would grant citizenship rights to an estimated 10 million illegal aliens currently in the country and allow them to collect Social Security benefits for work they performed while illegally employed in the U.S. The bill also grants complete amnesty to employers who have drawn the estimated 12 million aliens to the U.S. by illegally providing them with jobs.

In addition, an estimated 2 million new foreigners will be admitted to the country annually under the bill, more than doubling the current flow of legal immigration...

The 3 million [from the 1986 amnesty] became citizens, the border wasn't secured, immigration laws were not enforced and those 3 million were replaced by the estimated 12 million who are the subject of the current bill...