Current law requires Congress to convene for a joint session on Jan. 6 after a presidential election to count and ratify the 538 electoral votes certified by the 50 states and District of Columbia. The vice president, serving as president of the Senate, has the duty to count the votes in a joint session of Congress. 

In 2021, Mr. Trump pressured then-Vice President Mike Pence to reject some electors unilaterally. Mr. Pence refused, saying such a move was beyond his power. After Mr. Trump urged his supporters to march on the Capitol in a speech on the Ellipse, a pro-Trump mob overran the Capitol, temporarily interrupting the proceedings. After Congress reconvened, 139 House Republicans and eight Senate Republicans voted against certifying the election results. 

The new legislation would make it clear that the vice president’s role is merely to count the votes publicly and that he or she has no power to alter the results. It also would significantly raise the threshold to sustain an objection to a state’s electors to one-fifth of both chambers, up from one House member and one senator now. 

The proposal would also provide for an expedited federal court challenge if a state attempts to delay or tamper with election results. The bill holds that the court decision is final and requires Congress to accept that decision.

The current Electoral Count Act “is a time bomb under democracy, and we learned on Jan. 6 that its ambiguities and confusing terms are very dangerous,” said Maine Sen. Angus King, an independent who caucuses with Democrats.

Sen.

Susan Collins

(R., Maine) credited the work of a group of 15 senators who span the ideological spectrum in negotiating the bill. “The events of Jan. 6 clearly brought home the flaws in the law,” she said.

The Biden administration called the changes “a vital piece of legislation.”

Sen.

Josh Hawley

(R., Mo.) said he opposed changes to the current law. Mr. Hawley was the first senator to say he would object to the results of the 2020 presidential election, a move that forced lawmakers to debate and vote to affirm the states’ tallies on Jan. 6, 2021. As Mr. Hawley entered the Capitol ahead of the joint session that day, he was photographed fist-pumping to cheers from the pro-Trump crowd gathered outside.

“I think it’s fine, this is the democratic process,” Mr. Hawley said about the current rules. “I don’t think the objection caused the riot.” 

Other lawmakers have used the process outlined in the Electoral Count Act to object to election results in recent years. Some Democrats objected, unsuccessfully, to certification of both of former President

George W. Bush

‘s wins as well as Mr. Trump’s.

In both cases the Democratic nominee for president had already conceded and wasn’t supportive of the objections. Mr. Trump has continued to call for overturning the results and to claim falsely that he won the 2020 election.

The House select committee investigating the Jan. 6 attack made four criminal referrals for Mr. Trump to the Justice Department on Monday after investigating the lead-up and attack itself. Mr. Trump has denied wrongdoing related to the riot. The Justice Department is currently conducting a parallel investigation of the events.

“I don’t care whether they change The Electoral Count Act or not, probably better to leave it the way it is so that it can be adjusted in case of Fraud,” Mr. Trump said in a post on Truth Social on Tuesday.

Mr. Trump has said the planned changes show that the vice president did indeed have the power to block electors under current law. Backers say they are trying to eliminate any loopholes that could be exploited by future candidates, including Mr. Trump.

Among the Electoral Count Reform Act provisions included in this week’s spending package is a requirement that each state’s governor, unless specified in the state’s laws or constitution, submit the slate of electors. That would keep states from submitting false electors as some sought to do in 2020. 

It also would prevent state legislatures from overriding the popular vote in their states by declaring a “failed election,” except in narrowly defined “extraordinary and catastrophic” events.

Edward Foley, the director of Election Law at Ohio State University said the bill’s most significant provision is making sure the courts are the final backstop in case of false electors.

“We can look to courts as being the branch of government that is most immune from this kind of political denialism,” he said.

The version included in the spending bill is the Senate version, which had 38 co-sponsors, including both Majority Leader

Chuck Schumer

(D., N.Y.) and Minority Leader

Mitch McConnell

(R., Ky.).

In September, the House passed its own version of the legislation, 229-203. Nine Republicans joined Democrats in voting to pass the House bill. None of them are returning to Congress next year.

Write to Eliza Collins at eliza.collins@wsj.com and Lindsay Wise at lindsay.wise@wsj.com