Democrats are pushing what may be their last chance to hold off voter suppression efforts by Republicans, and say that their control of both the House and Senate is at risk if they do not pass their new legislation to protect elections.

Their bill, which cleared the US House on a party-line vote last week, has now been taken up by a bitterly divided Senate. It would ensure that states with a recent history of voter suppression must obtain federal approval before making any changes to their election systems, while also undoing a recent supreme court decision that makes it harder to challenge laws under the Voting Rights Act.

But Democrats appear unlikely to get more than a handful of GOP votes in the Senate on the bill. They need the support of 10 Republicans to overcome the filibuster, the procedural rule requiring 60 votes to advance legislation. Just one Senate Republican, Lisa Murkowski of Alaska, has said she supports reauthorizing the provision, an early signal of how difficult it will be to get Republicans to sign on at a time when state party members are pushing more voting restrictions.

Outside groups continue to escalate pressure on members of Congress to pass the bill, which is named after John Lewis, the civil rights icon. They held marches in Washington on Saturday – the 58th anniversary of the historic march on Washington, where Martin Luther King Jr gave his I Have A Dream Speech.

Theodore Dean, 84, attended the 1963 march and drove 16 hours from Alabama to attend the march for voting rights in Washington on Saturday.

“I’m here because I got grandchildren and children,” he said. He added that the fight over voting rights “gets worse every year. Sometimes it feels like it goes down instead of up. My children and grandchildren need to be able to vote too.”

Democrats have highlighted the importance of passing voting rights legislation since the beginning of the year, but the bill arrives in the Senate at a moment when the stakes are uniquely high. State lawmakers are currently drawing maps for electoral districts that will be in place for the next decade. Unless the bill passes, it will be the first time since 1965 certain states with a legacy of racial discrimination won’t have to get their district approved before they go into effect. That could encourage state lawmakers to draw districts that make it harder for Black and other minority voters to elect the candidate of their choice, critics say.

The blockade also underscores how Democrats have not yet found a way to deal with the filibuster. Even amid loud calls to do away with the process, a handful of moderate Democrats, led by Joe Manchin of West Virginia and Kyrsten Sinema of Arizona, have refused, holding up Democratic efforts to pass voting rights protections, among other measures.

“The same people who are suppressing the vote are also using the filibuster to block living wage – it’s not about one issue,” said the Rev William Barber, a co-leader of the Poor People’s Campaign and a civil rights leader. “Anyone who tries to make this about one issue like voting rights, you’re misleading the people. You have to draw this line and connect the dots.”

There are also fraught political stakes for Joe Biden. Amid growing concern the White House wasn’t taking the fight for voting rights seriously enough, the president gave a public speech on the topic in July. Still, White House advisers have said they believe they can “out-organize” voter suppression, an idea that has infuriated civil rights leaders.

“You said the night you won that Black America had your back and that you were going to have Black America’s back,” the Rev Al Sharpton, the civil rights leader, said at the rally in Washington on Saturday. “Well, Mr President, they’re stabbing us in the back. In 49 states, they’ve got their knives out stabbing us in the back.

“You need to pick up the phone and call Manchin and others and tell them that if they can carve around the filibuster to confirm supreme court judges for President Trump, they can carve around the filibuster to bring voter rights to President Biden,” he added.

“We have a problem here. We have Republicans on one side saying the bill isn’t needed,” said Derrick Johnson, the president of the NAACP. “And then we have far too many Democrats who lack the sense of urgency that it’s going to be absolutely critical to protect the rights of voters.”

Republicans successfully filibustered a different voting rights measure earlier this year – one that would prohibit partisan gerrymandering, as well as require same-day, automatic and online voter registration. But Derrick Johnson, the president of the NAACP, said he was confident this bill would actually pass.

“I don’t think we’re gonna have the same fate with this piece of legislation that we’ve seen, being stalled in the Senate. I do believe there will be the necessary political will to pass it,” said Johnson, who has met with the White House and members of Congress to push for the bill. Pressed on whether he believed 10 Republicans would sign on to the bill, Johnson suggested Democrats could do away with the filibuster to pass the bill.

“I’m not suggesting it’s gonna require 10 Republicans. I am suggesting the legislation will pass,” he said. “I don’t see a doomsday. I see a reality that voting rights protections must pass before the end of this year … Our democracy will be in shambles if it’s not done.”

A Republican filibuster of the John Lewis bill could offer Democrats wary of getting rid of the rule one of the clearest examples to date of how it has become a tool of obstruction. The last time the Senate voted to reauthorize the Voting Rights Act in 2006, it passed 98-0 before being signed by George W Bush, a Republican.

“This iteration of the Voting Rights Act, this should be something that should garner bipartisan support. And if it garners none, and if there’s not even a serious conversation about tweaks to get to a deal, then I think that tells us something,” said Damon Hewitt, the president and executive director of the Lawyers’ Committee for Civil Rights Under Law, a group that strongly supports the bill.

“It tells us that there was never really an attempt to play ball. Or, even if there was some attempt, there was just insufficient political will,” he added.

Texas Democrats also heightened the stakes when they fled the state capitol last month to thwart Republican efforts to pass new sweeping voting restrictions. The Texas lawmakers spent much of the last month in Washington lobbying to pass federal voting protections. The standoff ended last week when the Texas bill passed; if Congress fails to act on its own legislation now, it could make the effort from Texas lawmakers look futile.

In Washington on Saturday at the march, there was a sense of history and an awareness of how the fight for voting rights now mirrored the struggle of the civil rights movement.

“Our ancestors did these marches and did these walks and talk – so this is like something that I’m supposed to do,” said Najee Farwell, a student at Bowie State University.

“It’s kind of changed but you still can see the same stuff going on. If you look at pictures back from 1950 it’s still the same stuff going on right now,” said Jemira Queen, a fellow student.