Democrats say there’s little to be gained from staging a fight this week over the Electoral College vote count, ignoring calls from activists that want lawmakers to use “any and every” opportunity to let President-elect Donald Trump and Republicans know they will face opposition on Capitol Hill.

The House and Senate on Friday are scheduled to certify the state electoral vote counts, giving members a final chance to raise objections to Mr. Trump’s 306-to-232 Electoral College victory over Hillary Clinton.

But there appears to be no momentum for a challenge, even from lawmakers that supported similar efforts in the past.

“I have not heard anything,” said Rep. Raul M. Grijalva of Arizona, co-chair of the Congressional Progressive Caucus, who was part of a 2005 effort to challenge the vote for George W. Bush. “Usually someone will say, ‘Does anybody want to join me?’ That hasn’t happened.”

Rep. James E. Clyburn of South Carolina, who was also part of the 2005 effort, told The Washington Times he’s not heard of any movement to try to deny Mr. Trump the White House. Asked whether he would support such an effort, Mr. Clyburn said, “No.”

That is disappointing news for outside groups and activists that want Democrats to make life hard for Mr. Trump and the GOP-controlled Congress.

“It seems to me that Democratic lawmakers have an even heavier responsibility and should seize any and every opportunity to send a message to the Republican Party letting them know that the next four years will not be a case of ‘roll over and play dead’ but one of checks and balances and accountability — starting with voter suppression and foreign involvement in the election,” said Shannon Gattens, a community activist from New Jersey.

Ms. Gattens is among more than 850 people that have signed an online Change.org petition being circulated by a group called United for America, PA that is calling on lawmakers to raise objections to the Electoral College count as a way to spark a debate over “discriminatory voter ID laws which disenfranchised voters of color across the country” as well as probing Russia’s involvement in the election.

The petition is directed at Reps. John Lewis of Georgia and Theodore E. Deutch of Florida, as well as Sen. Patrick J. Leahy of Vermont and former Sen. Barbara Boxer of California, who was the sole senator to back the 2005 objection, and did not seek re-election last year.

Vice President Joseph R. Biden, in his role as president of the Senate, is slated to preside over the joint session of Congress that has been called to certify the electoral vote counts for each of the states, which were tallied last month.

The process has typically been symbolic, but there have been instances in which lawmakers from the House and Senate team up, as required under the law, to challenge the results, forcing both chambers to consider the objections separately.

In 2004 Democrats questioned “irregularities” in the counting of Ohio’s electoral votes.

Their challenge was rejected in both the House and the Senate, clearing the way for the joint session to confirm Mr. Bush’s win.

At the time, lawmakers backing the effort said the goal of their long shot effort was to focus more attention on the need for election reform and on the disenfranchisement of voters in the election.

Mr. Grijalva said Tuesday he understands how lawmakers might want to express their frustration with Mr. Trump or the fact that the Republican won despite losing the popular vote to Mrs. Clinton.

“But that reality is the reality,” he said. “It is done — you know?”

Rep. Ruben Gallego, another member of the Congressional Progressive Caucus, said he is moving on.

“I think, obviously, the election did not have the outcome that any of us wanted, but at this point, we have to make sure we keep focused on making sure that we keep Trump and the Republicans held accountable,” Mr. Gallego, Arizona Democrat, said. “So I don’t think objecting to the Electoral College vote will do anything.”

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