After the Senate failed to pass a health care bill that President Trump wanted them to, Trump, as has become common for him, went to Twitter to deflect blame. He tweeted early Saturday morning (doesn't he ever sleep in?) with a demand that the Senate change the rules to pass health care. According to Trump, the health care bill failed because of the filibuster rule requiring most important legislation to get 60 votes in the Senate, not 51 (or 50 with a tie-breaking vote by the Vice President).
Trump's tweets connecting the health care loss to Democrats stopping them from getting 60 votes are a little bizarre—the health care bill that failed in the Senate early on Friday morning went down 49-51, with three Republicans joining the Democrats in opposing it. And for some of the other agenda items that Trump could have trouble passing—most notably funding for the border wall—might still have just as much trouble getting to 51 votes.
But Trump does have a point—the health care fight would probably have been a little easier if Republicans could do whatever they wanted with 51 votes. Republicans were trying to repeal Obamacare through a parliamentary procedure called budget reconciliation, which lets budget changes be passed with just 51 votes, but not regulatory changes. For this reason, many of Republicans' favorite changes to the health care system were not included in any of the bills that failed. And even some of the stuff that was initially included—like defunding Planned Parenthood—caused problems with the Senate parliamentarian for seemingly breaking the Senate rules. Maybe if the health care bill could have included all they wanted it to, Republicans would have been able to pass something. But that would have also required Republicans agreeing on what they wanted, which they never seemed to do.
President Trump also continues to blame Senate Democrats for his problems, he also tweeted that if the Democrats were in control of the Senate, they would get rid of the filibuster.
But recent history suggests that just isn't true. Democrats controlled the Senate from 2006 to 2014, and they allowed the filibuster to remain in place for legislation (though they eliminated it for nominees below the Supreme Court level in 2013). President Obama's biggest legislative achievements—the stimulus package to fight the Great Recession, the Dodd-Frank financial reform package, and of course Obamacare itself—all passed with 60 votes.
It was arguably Mitch McConnell as Republican minority leader starting in 2007 who turned the filibuster from an uncommon parliamentary procedure to the threshold needed for all major bills. And as a result, there are likely more laws that Democrats would have passed under Obama with just a 51-vote threshold than Republicans would pass now.
It doesn't look like the legislative filibuster is going anywhere...yet. Earlier this year, Senate Republicans "nuked" the filibuster for Supreme Court nominees in order to put Neil Gorsuch on the bench. But immediately afterwards, a bipartisan group of 61 senators wrote a letter to Senate leadership expressing their desire to keep it in place for legislation. For now, the procedure stays.