By Andrew Duehren and Kristina Peterson

WASHINGTON -- Republicans and Democrats on Capitol Hill are racing to finish a substantial to-do list before the end of the year, trying again to pass another coronavirus relief bill and seeking to avoid a government shutdown after a mixed result for the parties on Election Day.

Lawmakers and the Trump administration had paused negotiations on a relief bill until after the election, and Senate Majority Leader Mitch McConnell (R., Ky.) is set to take a more active role in the talks after Joe Biden defeated President Trump. Members of both parties say they are eager to pass another relief bill after months of delays, though the disagreements that plagued previous efforts persist.

Mr. McConnell said Tuesday that the two parties remain far apart on how large another package should be, as Democrats seek a bill topping $2 trillion and Republicans favor a $650 billion proposal.

"It seems to me the snag that hung us up for months is still there. I don't think the current situation demands a multitrillion-dollar package. I think it should be highly targeted," he said.

Virus cases are spreading rapidly across the country, raising the prospect of new restrictions on businesses that could hurt the economic recovery. Mr. Trump's role in any new talks remains unclear. He has declined to concede the presidential election, and his campaign is mounting legal challenges to the results.

Each party sees itself gaining an advantage in the new round of talks after the election, with Democrats bolstered by President-elect Joe Biden's victory and Republicans encouraged by their unexpectedly strong showing in congressional races across the country. The party picked up House seats, and Senate results show a GOP advantage of 49-48, after the party won North Carolina on Tuesday. Republicans are favored to win an outstanding seat in Alaska, and there are special elections in January to determine two Georgia races.

Talks between House Speaker Nancy Pelosi (D., Calif.) and Treasury Secretary Steven Mnuchin faltered for months and haven't restarted.

"The price of poker has changed after the election," said Sen. John Kennedy (R., La.). "I don't think Speaker Pelosi was ever holding the cards that she thought she was, but she's certainly not now."

Democrats haven't budged from their insistence on a broad package, with Mrs. Pelosi last week rejecting Mr. McConnell's call for a smaller bill. With the Georgia runoffs set to determine control of the Senate in January, some Democrats say Republicans will want to pass a major bill to bolster candidates in that state.

"I think Mitch McConnell has got to win two Senate seats in Georgia where people are hurting and need help," said Sen. Tim Kaine (D., Va.). The two races in January would "seem to make everybody want to do something in November to December rather than put it off until after."

Any new coronavirus relief bill is "going to be smaller than what was on the table before the election," said Rep. Tom Reed (R., N.Y.), co-chair of the bipartisan Problem Solvers Caucus, which had proposed a $1.5 trillion package. "Obviously a lot's going to depend on where the administration comes down and the president and his willingness to sign a package into law."

Mr. Biden has pushed for Congress to pass a fifth relief bill, and some Democrats indicated that Congress could always take up yet another package next year after they take control of the White House.

"After President Biden takes the oath, I think you could address stimulus and infrastructure and climate change simultaneously," Rep. Richard Neal (D., Mass.), the chairman of the Ways and Means Committee, said.

Mr. Biden, who has longstanding relationships with congressional leaders, could play a bigger role in the stimulus discussions during the lame duck to help pave the path for an agreement before he takes office.

Biden campaign spokesman Jamal Brown said Mr. Biden believes that lawmakers should "come together and take action on immediate relief for the American people. If Congress will not act imminently, he will start working to pass relief the moment he's sworn in."

Most of the direct assistance Congress enacted earlier this year, including enhanced jobless benefits and emergency aid for small businesses, has expired or is about to in the coming weeks.

Beyond the overall price tag, Republicans and Democrats have disagreed for months about how much aid to send to state and local governments and the size of a federal supplement to jobless benefits. Funding for schools, for vaccine distribution, and small businesses have all held up by the standoff.

Meanwhile, funding for government operations runs out after Dec. 11, and Senate Republicans released their proposed spending legislation on Tuesday. While both parties have said they want to reach an agreement on yearlong spending legislation, they will likely ultimately pass another stopgap measure. That could leave funding the government as an early task of the Biden administration.

Another looming task is passing an annual defense-policy bill. The House and Senate have each passed their own versions of the bill, but have yet to negotiate a compromise bill to pass both chambers. The biggest hurdle could be Mr. Trump's opposition to provisions in both bills that would rename military bases honoring the Confederacy.

The Senate bill includes a bipartisan provision sponsored by Sen. Elizabeth Warren (D., Mass.) that would require the military to change the names of all bases and other military assets named for Confederate commanders within three years -- language President Trump has repeatedly said would prompt him to veto the massive must-pass bill.

Both the House and Senate passed the defense bills this summer with more than the two-thirds supermajority needed to override a potential veto.

--Kate Davidson and Richard Rubin contributed to this article.

Write to Andrew Duehren at andrew.duehren@wsj.com and Kristina Peterson at kristina.peterson@wsj.com

Corrections & Amplifications

This story was corrected at 9:56 p.m. ET. The originalmisstated the bipartisan Problem Solvers Caucus' proposed coronavirus relief package as $1.5 billion The proposed amount is $1.5 trillion.

(END) Dow Jones Newswires

11-10-20 1657ET