[With less than 60 votes, if my understanding is correct, then they will never get to vote on the bill because they will not have the votes for cloture or to end the debate on the floor.]
According to the rules, correct.
But it seems the Democrats are planning to break the Senate rules. Since they know they can’t get the Senate bill passed in The House, as is, they are going to use the budget reconciliation process to pass a different House bill and then modify the Senate bill to merge the two together. According to the rules, they would then need to pass the new bill again in the Senate with 60 votes, but since budget bills only need 51 votes they plan to pass it as if it were a budget bill. ILLEGAL - but this is their plan.
They won't go through reconciliation until they get the promise of future corrective action from the Senate. Why anyone would accept a Democratic Senate promise is beyond me.
According to post 7, there is no cloture or 60 vote requirement, only 20 hours of debate followed by amendments to the bill where at that time the Republicans can inundate the measure with numerous amendments requiring a vote on each one.. Michele Malkin is calling it a “vote-a-rama”.