According to this answer citing the senate website:
Senate rules also permit a measure to be placed directly on the calendar when introduced or received from the House. This process permits senators to bypass referral to a committee they believe unsympathetic. Alternatively, if a committee fails to report a measure, a new measure with exactly the same provisions may be introduced and placed directly on the calendar.
If so, how has McConnell managed to block the House Bill twice?
Look a little further down in the next paragraph of the article quoted from that post and you will see this. I am responsible for the highlighting.
The Senate accords its majority leader prime responsibility for scheduling. He may carry out this responsibility by moving that the Senate proceed to consider a particular matter. By precedent, he and the minority leader are recognized preferentially, and by custom only he (or his designee) makes motions or requests affecting when the Senate will meet and what it will consider.
Notice that this is BY PRECEDENT only and only to prevent a chaotic amount of bills from being introduced. Any member of the Senate can introduce something to the floor. This can be prevented by objection of any member of the Senate.
This marks the third time that McConnell has blocked House-passed government funding bills in the past two weeks. Under Senate rules, any senator can ask for consent to vote on or pass a bill, but any senator can object.
Referenced here.
