People trying to eliminate the Senate filibuster have been quite noisy recently; given that the filibuster has been a practice allowed by rules in the Senate for 215 years, and given recent attempts to argue against the Electoral College, the Senate, the authority of Congress over the District of Columbus, the authority of states to determine their own election laws, and then some, it's very hard to avoid the feeling that people have just been running through all longstanding American institutions to see which can be destroyed in order to 'save American democracy'. I've noted before that attacks on the Senate as 'undemocratic' don't actually make all that much sense; attacks on the filibuster as 'undemocratic' don't make much sense, either. The filibuster is a legislative rule; no legislative rules are determined democratically. Nor does it make any sense to say that it is undemocratic because by means of it a minority of legislators can force a majority to work with them rather than simply force things past them all the time. Forcing legislators to work together reduces the oligarchical tendencies of legislatures and increases the quality of that legislature's representation of the people. Nor does history show the filibuster to be any kind of definitive act; it is a cooling-down measure. Most filibusters only delay things for a day or two; those that are successful are often overcome simply by regrouping or renegotiating. If we go back to its early beginnings, when Cato the Younger used the Roman equivalent of the filibuster to block several of Julius Caesar's attempts to seize an ever-expanding power, it didn't actually prevent Caesar from seizing power; but it was successful at slowing him down and forcing him to regroup. The filibuster can't actually stop anything in the long run, so attacks on it are often overblown; and that it's 'bad for democracy' to have a mechanism for slowing down controversial seizure of power is not as obvious as many of its critics suggest.
In any case, we know more or less what will happen if the filibuster is eliminated in the Senate; Senators will find other ways to throw gears into the works, because in fact, raising obstacles in order to force re-negotiation is one of the ways legislative business is conducted in every legislature that has ever existed. The House had the filibuster for a long time, but eliminated it (actually it went back and forth on eliminating it for a while). Then the Representatives started messing with the quorum, which went on until the rules were changed to rule that out. This, however, only made the routes more indirect; today, minorities in the House largely slow things down by horse-trading within committees, interfering with votes for bills brought up under suspension of rules, motions to recommit, and the like. Unless you insist on an up-down vote for everything, you aren't going to eliminate shenanigans in a legal forum filled with lawyers. The real question is whether what would replace the filibuster would actually be an improvement. I don't think it's clear that the elimination of the filibuster by the House was an improvement; I think it can be argued, for instance, that House legislation became considerably more erratic after the loss of the filibuster. But in any case, it's always important in these matters not to focus only on what you see now but on what you don't see -- whatever things that wait in the wings to replace it.