Framers of the Constitution, such as Alexander Hamilton and James Madison, spoke out against the concept of parties, and the Constitution does not mention them. See for example https://www.history.com/news/founding-fathers-political-parties-opinion . Therefore, how did we arrive at the situation where the leader of the majority party in the Senate has the enormous power to call issues to a vote? How does this power trace ultimately back to the Constitution?
Article I, Section 5 says
Each House may determine the Rules of its Proceedings ...
That gives both the House and the Senate wide latitude to adopt whatever rules those bodies choose. The Senate, for example, has adopted rules that allow for the fillibuster while the House has not. In general, the House has adopted rules that give more power to the Speaker of the House and other leaders than the Senate gives to leaders in that chamber.
Nothing stops either chamber from amending their rules. Either chamber could, for example, adopt a rule that allows any member to force a vote on any proposition they like. Practically, however, the more people that have the ability to call (or prevent) votes, the more difficult it is to get any legislation passed. If individual members could force votes whenever they wanted, they could force hundreds or thousands of votes on amendments to a single bill which would tie up the chamber in votes for weeks or months. They could likely sabotage many pieces compromise legislation by forcing members to vote on every unpopular element individually in a bid to make the overall legislation less appealing. For example, when the Senate was considering Obamacare, there were a number of elements designed to shore up support for the legislation from a handful of wavering Senators. Among those elements was the "Cornhusker kickback" which gave Nebraska preferential treatment in order to ensure Sen. Ben Nelson voted for the entire bill. It would have been very tough for that element to have survived an up-or-down floor vote but it would have been very tough for the entire bill to have passed without it.