It's my understanding that a single senator can't just filibuster anything they want unless the conditions are right. It depends on a few different factors and requires the bill to be brought to the floor for debate, which itself would require cooperation from the majority leader. That's not likely to happen.

Filibuster what, exactly? No proposal is before the Senate...

ON edit: Oops, sorry, 702 is up for renewal. Still not clear he could win a cloture vote, though.

If you're solo you have to actually stand up and talk still it seems. (And even then a 60+ person majority can vote to close the debate on you) Nobody has done it solo for more than 24 hours or so. Presumably at that point you're about ready to keel over.

He needs 40 other Senators to agree with him; 60 votes can close debate and stop a filibuster.