The CNN anchor said Democrats had been "outmaneuvered" by the Senate minority leader, as he questioned the balance of the Supreme Court.
The advocates of changing the current system essentially think we need to let the government do more.
The filibuster, as it exists, has been used over and over and over again to suppress the will of the people who have elected people to advance workers' rights.
"I'd like to restore the Senate to what it was, where we actually had debates and people had to hold the floor," Maine Senator Angus King said.
The Senate shot down another attempt at overhauling U.S. voting rights laws on Thursday in a party-line vote.
"It got to the point where senators on both sides were pleading for leadership to fill the void and protect our citizens. I stepped up," McConnell said.
The U.S. risks default for the first time in history if Congress doesn't raise the debt ceiling by October 18.
The Utah senator's comments come during a stand-off with Democrats over an unprecedented U.S. default.
"It's a real possibility," Biden told reporters outside the White House.
The Arizona Democratic Party accused Sinema of protecting a "Jim Crow relic" under the guise of bipartisanship.
To do away with the filibuster, it would require the vote of all 50 Democratic Senators, plus a tie-breaking vote from Vice President Kamala Harris.
"We will not sit back and allow you to filibuster our right to vote," the civil rights leader said at a rally in Washington, D.C.
"Time for them to get to the Capitol and do the job they were elected to do," Gov. Abbott tweeted.
Democratic Sen. Joe Manchin previously said he would not vote to "weaken or eliminate the filibuster."
The conservative commentator praised the Arizona lawmaker for "holding the line on the filibuster" at a rally in Phoenix.
"We're going to continue to push. We're going to have hearings. We're going to have votes until we get this done," the Democratic Senate Majority Leader said.
Biden agreed with CNN moderator Don Lemon that the filibuster is "a relic of Jim Crow" that has been used to fight against civil rights legislation historically.
Trump also took issue with McConnell's inability to persuade Senator Joe Manchin to join the Republican Party.
The MSNBC host said Sinema shouldn't "allow" the late congressman's work to "die."
"Pick up the phone and tell Joe Manchin, 'Hey, we should do a carveout.' I don't care whether he does it in a microphone or on the telephone — just do it," the House Majority Whip said.
We have elections for a reason. Yet our own Congress is hamstrung by a privileged few that decide to block everything, to play political games.
The representative for Georgia said the Democrats' bill aiming to drastically change election and voting laws was "horrible."
Every GOP senator voted against the move to debate the For the People Act. After the filibuster, Majority Leader Chuck Schumer said: "We will not let it die. This voter suppression cannot stand."
All 50 members of the Senate Democratic caucus voted in favor of the bill, including Democratic West Virginia Senator Joe Manchin who was considered a lone holdout.
"We thank you for co-sponsoring the Equality Act, and we urge you to take the necessary next step of ending the filibuster so queer and transgender civil rights can pass the Senate and be signed into law," the letter to Sinema, the nation's first openly bisexual senator, reads.
The Arizona senator argued that abolishing the filibuster could lead to reversals of progressive legislation and affect such programs as Medicare or Medicaid.
The coalition of 101 California progression groups pressured Feinstein to support nixing the filibuster ahead of the Senate's Tuesday test vote on the For the People Act.
"How do you go forward right now in this moment in history and not address the terrible climate crisis that we face and transform our energy system?" the Vermont progressive asked Sunday.
On a private call on Monday, Manchin suggested he would be willing to change the Senate rules so Senate Democrats could pass legislation with fewer than the 60 votes currently required by the filibuster.