Biden last week appeared to call out Manchin and another moderate Democratic senator, noting that Republicans remain almost universally opposed to the pieces of legislation and are joined by two Democrats he declined to name.
Democrats have pushed the legislation as the antidote to a wave of restrictive state voting laws sweeping the country, many inspired by former President Donald Trump's false claims of fraud in his 2020 election loss.
"We now are witnessing that the fundamental right to vote has itself become overtly politicized", Manchin wrote in a Charleston Gazette opinion essay.
"Voting and election reform that is done in a partisan manner will all but ensure partisan divisions continue to deepen", he wrote.
Republican senators last month successfully filibustered legislation creating a January 6 commission; Manchin and 53 other senators voted for such group to investigate the insurrection at the U.S. Capitol led by Donald Trump supporters.
Jones' criticism may not be the only backlash Manchin receives from within his own party - Axios' Jonathan Swan reports that House progressives are becoming "fed up with efforts to accommodate Republican senators", though it seems unlikely that the senator will be influenced by the reactions.
Even if all 50 Democrats remain united, the withdrawal of seven from the Republican faction is not enough to defeat the filibuster.
He wrote: "My Republican colleague Senator Lisa Murkowski (Lisa Murkowski) joins me in urging the Senate leadership to update and pass the bill through regular orders".
The voting rights legislation would nullify many GOP-led voting restrictions passed in the states.
Biden said the right to vote was "precious" and must be protected, and pledged that June would be a "month of action" on Capitol Hill. Biden stated, "we know here, in this hallowed place, we simply can't bury pain and trauma forever and at some point there will be a reckoning, an inflection point like we're facing right now as a nation".
Kentucky Senate Republican leader Mitch McConnell has promised to thwart election bills that he considers to be excessive government intervention in the state's election system. "The failed vote in the Senate had six fearless Republicans, but that was four short of the ten necessary to advance the legislation", Manchin said May 28.
The House in March passed the For the People Act in a 220-210 vote. The legislation would restrict partisan gerrymandering of congressional districts, eliminate hurdles to voting and bring transparency to a campaign finance system that allows wealthy donors to anonymously bankroll political causes.
This measure has been a priority for Democrats since it won a majority in the House of Representatives in 2018. But it has taken on added urgency in the wake of President Donald Trump's false claims about the 2020 election, which incited the January 6 riot at the Capitol.
Fox News Sunday moderator Chris Wallace said that threatening to vote against filibuster could motivate Republicans to negotiate the bill.