Currently a single Senator can stop vote on any legislation by simply expressing a desire to Filibuster. There does not exist a requirement to show commitment or support in the minority to overcome this block on voting. The burden resides with the majority to gather 60 votes to move the legislation along to a vote on the Senate floor.
There is a reason why the minority is called that. A minimum vote of 40 should be required to continue the Filibuster, forcing the minority to keep enough votes on the floor at all times. There should be an allowance for one or many Senators in the minority to express displeasure with a pice of legislation, however, the burden should be on the minority party to support the difference of opinion.