The Alito Vote Tally,
according to Ed Whelan at Bench Memos:
I believe that 86 senators have now declared their positions: 55 for Alito, 31 against. Of the remaining Democrats, four (Conrad, Dorgan, Landrieu, and Pryor) are possible yes votes.

So it looks like Alito will get between 56 and 62 votes — probably 58 to 61.
The vote is currently scheduled for next Tuesday.