The proposed laws would seek to remove hurdles to voting which were enacted in the name of election security.
US president Joe Biden has all but conceded defeat for this year on the Democrats’ elections and voting rights legislation.
Mr Biden declared he will not give up, but he is now talking more about future efforts.
The president spoke at the US capitol on Thursday after a key fellow Democrat, senator Kyrsten Sinema of Arizona, dramatically announced her refusal to go along with changing senate rules to muscle past a Republican filibuster.
Senate majority leader Chuck Schumer is still hoping to use senate procedural rules to bypass the blockade and force a floor debate.
But the Democrats still lack the support within their own party to overhaul the rules and pass the bill with a simple majority.
The Democratic package of voting and ethics legislation would usher in the biggest overhaul of US elections in a generation, removing hurdles to voting enacted in the name of election security, reducing the influence of big money in politics and limiting partisan influence over the drawing of congressional districts.
The package would create national election standards that would trump the state-level Republican laws. It would also restore the ability of the US justice department to police election laws in states with a history of discrimination.
Mr Biden had come to the capitol to prod Democratic senators in a closed-door meeting, but he was not optimistic when he emerged.
He vowed to keep fighting for the sweeping legislation that advocates say is vital to protecting elections.
“The honest to God answer is I don’t know whether we can get this done,” Mr Biden said.
He told reporters, his voice rising: “As long as I’m in the White House, as long as I’m engaged at all, I’m going to be fighting.”
Ms Sinema all but dashed the bill’s chances minutes earlier, declaring just before Mr Biden arrived on Capitol Hill that she could not support a “short-sighted” rule change.
She said in a speech on the senate floor that the answer to divisiveness in the senate and in the country is not to change filibuster rules so one party, even hers, can pass controversial bills.
“We must address the disease itself, the disease of division, to protect our democracy,” she said.
The moment once again leaves Mr Biden empty-handed after a high-profile visit to US congress.
Earlier forays did little to advance his other big priority, the “Build Back Better Act” of social and climate change initiatives.
Instead, Mr Biden returned to the White House with his agenda languishing in congress.
The US president spoke for more than an hour in private with dissenting Democrats in the senate, including Joe Manchin of West Virginia, who also opposes changing senate rules.
Mr Manchin said in a statement later: “Ending the filibuster would be the easy way out. I cannot support such a perilous course for this nation.”
Both senators went to the White House on Thursday evening for an additional hour, which the White House later described as “a candid and respectful exchange of views”.
Since taking control of congress and the White House last year, Democrats have vowed to counteract a wave of new state laws, inspired by former president Donald Trump’s false claims of a stolen election, that have made it harder to vote.
But their efforts have stalled in the narrowly divided senate, where they lack the 60 votes out of 100 needed to overcome a Republican filibuster.
For weeks, Ms Sinema and Mr Manchin have come under intense pressure to support rules changes that would allow the party to pass their legislation with a simple majority – a step both have long opposed.
Senate minority leader Mitch McConnell called Ms Sinema’s speech an important act of “political courage” that could “save the senate as an institution”.
Her own colleagues were not so charitable. Senator Angus King, a Maine independent who once opposed changing the senate rules, said: “She believes that the risk of changing the filibuster is greater than the risk of what’s going on in the states.
“I hope profoundly that she’s right. I fear that she’s wrong.”
