WASHINGTON — Representatives Marjorie Taylor Greene and Lauren Boebert are two backbench freshmen in the House minority, powerless in the official hierarchy and unlikely to gain much power even in a likely Republican majority next year.

But their antics, violations of decorum and association with white nationalists have elevated their profile far beyond their positions, and Democratic operatives are determined to make them the face of the Republican Party in the looming election season.

The two are not the only Republicans bringing unwanted attention to the party, and some of the division in the party’s ranks is being amplified by internal disputes, not by Democrats. Senator Rick Scott of Florida, the chairman of the Senate Republicans’ campaign arm, earned a public rebuke this week from Senator Mitch McConnell of Kentucky, the Republican leader, for putting out a campaign manifesto that called for raising taxes on the poor and cutting Social Security.

On Wednesday, a little-known Republican, Representative Van Taylor of Texas, abruptly dropped his re-election bid after operatives on the party’s right flank — angered by his vote to create a bipartisan commission to examine the Jan. 6, 2021, attack on the Capitol — revealed pornographic text messages that he had sent to a paramour.

But it is the faces of Ms. Boebert of Colorado and Ms. Greene of Georgia that are splashing across social media, political videos and advertising, after they both stood and heckled President Biden during his State of the Union address on Tuesday. Ms. Boebert shouted at the president just as he was referring to the death of his son Beau Biden.

Not since President Donald J. Trump used racially charged language in 2019 to castigate the liberal women of color in “the Squad” have freshmen House members received quite so much attention. Representative Ilhan Omar, Democrat of Minnesota and Mr. Trump’s favorite Squad target, said there were big differences.

For one, Ms. Boebert and Ms. Greene intentionally provoke responses to stay front and center, she said, while she and Representatives Alexandria Ocasio-Cortez of New York, Ayanna Pressley of Massachusetts and Rashida Tlaib of Michigan were more often sought out by critics.

On Monday, Ms. Greene was publicly rebuked by the House Republican leader, Representative Kevin McCarthy of California, over her appearance at a far-right conference with ties to white supremacy. The next day, she and Ms. Boebert heckled Mr. Biden and tried unsuccessfully to strike up a chant of “build the wall” during his State of the Union address.

And while Democrats routinely condemn their own for statements they consider out of the mainstream, Republicans rarely do, instead providing Ms. Greene, Ms. Boebert and others on the far right with platforms to broadcast their messages, such as the recent Conservative Political Action Conference in Florida.

“With us, the opinion pieces by Democratic pundits are already prewritten, and there’s a lot of scolding that happens within the caucus,” Ms. Omar said. “That’s not what happens with their party.”

Mr. McCarthy did say that Ms. Greene’s appearance at the far-right conference was “appalling and wrong,” promising to have a talk with her, but that does not compare to the criticism that rained down on Ms. Omar when she used an antisemitic trope to suggest that support for Israel was driven by money. Mr. McCarthy has also said Ms. Greene will be given back the committee assignments that Democrats stripped from her if Republicans control the House next year.

Speaker Nancy Pelosi, at her weekly news conference on Thursday, repeated perhaps the only criticism that a Republican leveled at Ms. Boebert and Ms. Greene after their heckling at the State of the Union.

“Let me just say this,” Ms. Pelosi said. “I agree with what Senator Lindsey Graham said: ‘Shut up.’”

Republican leaders have an easier political task than Democrats as they seek to keep voters focused on what they are seeing in their daily lives, such as inflation, soaring energy prices and ongoing frustrations with the coronavirus pandemic.

“Democrats don’t have a clue what moves voters and are desperately trying to distract from their record of higher prices, soaring crime and a crisis along our southern border,” said Michael McAdams, the communications director for the National Republican Congressional Committee.

Ms. Boebert’s staff did not respond to requests for comment, and Ms. Greene declined to speak to The New York Times. But she has remained defiant in the face of criticism. In December, she told the former Trump adviser Stephen K. Bannon, “We are not the fringe; we are the base of the party.”

For that reason alone, Democratic operatives say they have every right to elevate the visibility of Ms. Greene and Ms. Boebert and tie them to other Republicans who have refrained from criticizing them even as they have castigated the two Republicans serving on the committee investigating the 2021 attack on the Capitol, Representatives Liz Cheney of Wyoming and Adam Kinzinger of Illinois.

Representative Sean Patrick Maloney of New York, the chairman of the Democratic Congressional Campaign Committee, said the House Democrats’ campaign arm had not decided how central to make the two lawmakers in the coming campaign season.

The committee is “making investments where they do the most good,” he said. “If that means making them the face the party, we will do it. If it means ignoring them, we will do it, because the point is to win the House, not to win an argument.”

“But,” he added, “their actions are disgraceful, from attending white supremacy conferences to yelling at the president when he’s talking about his fallen son.”

Democratic allies are not so reticent. Jon Soltz, the chairman and co-founder of VoteVets, a liberal veterans organization, said the group was testing messages with voters to tie incumbent House Republicans in districts that lean Democratic to far-right figures in the Republican Party.

The attack might not work in conservative-leaning districts, he said, but it could against Republicans whose seats emerged from redistricting as more Democratic, such as Representative Nicole Malliotakis’s in New York and Representative Mike Garcia’s in Southern California.

“There’s some rather crazy rhetoric that comes out of their mouths, and behavior like you saw from them at the State of the Union,” Mr. Soltz said. “There are a lot of independents in suburban districts that might have leaned to Biden by five or six points, but Democrats now have to go get those voters back.”

Another Democratic political operation, American Bridge, is tying Ms. Greene to Herschel Walker, the former University of Georgia football star recruited by Mr. Trump to challenge Senator Raphael Warnock, Democrat of Georgia, this fall.

Jessica Floyd, the president of American Bridge, said on Thursday that the group’s efforts were crafted to make the midterm elections a choice between what she called a Republican Party of extremists against a Democratic Party focused on the economy and governance — not a referendum on Mr. Biden, whose approval ratings are dangerously low.

Voters “know and don’t like the sort of extreme positions that Marjorie Taylor Greene and Lauren Boebert embody,” she said.

She added, “That’s an opportunity for Democrats, and I think that we should seize on it.”