Sen. Elizabeth Warren isn’t as toxic as House Minority Leader Nancy Pelosi — yet — but Republican operatives are laboring to change that, saying they will use the run-up to the elections next year to try to make the rising liberal star too poisonous for Democrats to handle.
The Republican National Committee, the National Republican Senatorial Committee and Republican-aligned groups such as American Rising are testing out the depth of the anti-Warren sentiment, hoping to inject her into Senate races the way Republican operatives have made Mrs. Pelosi a drag for House Democrats.
At the very least, they hope to make vulnerable Democrats have to declare whether they side with Ms. Warren on some of her most liberal causes.
“Just like Nancy Pelosi, Elizabeth Warren is deeply unpopular with voters and her policies are out of step with a vast majority of Americans, and we think that will be an effective way to brand vulnerable Democrats,” said RNC spokesman Rick Gorka.
Mrs. Pelosi has been a staple of Republican attacks, and Republicans say using her against Democrats helped their party win several close special congressional elections this year.
Former Secretary of State Hillary Clinton has also been a favorite target for Republican campaigners, and now they are adding yet another woman to the list in Ms. Warren, whose approval rating is underwater in states such as Virginia and Missouri — where incumbent Democrats could face tough Senate elections next year.
Republicans said Ms. Warren appears to turn off voters more than Senate Minority Leader Charles E. Schumer of New York, who does not register much in polls, and Sen. Bernard Sanders, the Vermont independent whose populist message resonates in Trump-friendly states.
Whit Ayres, a Republican Party pollster, said Ms. Warren is less known than Mrs. Pelosi, but a concentrated messaging campaign could change that.
“Elizabeth Warren has that potential, but she doesn’t have it yet,” Mr. Ayres said. “It is not unusual for her name ID to be a good 15 to 20 points lower than Pelosi’s. It is not that she is unknown, but she is not as universally known as the former speaker.”
Ms. Warren’s office didn’t respond to a request for comment.
John McLaughlin, a Republican Party strategist, said injecting Ms. Warren into the races complicates things for fellow Democratic senators, who will either have to side with her, putting them on the liberal wing of the party, or else distance themselves, potentially angering the progressive base.
“Her liability is her radical ideas,” Mr. McLaughlin said. “If Republicans or a political opponent wants to make her a liability to more moderate Senate Democrats, they have to be able to attach those Democrats to some really radical ideas — including single-payer health care and higher taxes.”
The Democratic Senatorial Campaign Committee, the campaign arm for Senate Democrats, said Republicans are trying to draw attention away from their own failures.
“Republicans will try any desperate and ineffective tactic to try and distract from the fact that their toxic health care plan spikes costs and strips coverage from hardworking Americans,” said David Bergstein, a DSCC spokesman.
Both parties have sought to make their rivals into boogeymen in recent elections, to mixed results.
Democrats made modest gains in the House and Senate last year after trying to tie their rivals in congressional races to presidential candidate Donald Trump.
On their way to winning back the House in 2010 and Senate in 2014, Republicans framed races as referendums on Mrs. Pelosi, Mrs. Clinton, Senate Democratic leader Harry Reid and President Obama.
Ms. Warren’s national profile has been on the rise in recent months.
She was a top surrogate for Mrs. Clinton last year and a top critic of Mr. Trump, who returned the favor by calling her “goofy” and dubbed her “Pocahontas” in a jab over her claims of Cherokee Indian ancestry.
Ms. Warren garnered more national attention in early February after Senate Majority Leader Mitch McConnell, Kentucky Republican, cut her off in the middle of an attack on the chamber floor against Sen. Jeff Sessions, who had been nominated as attorney general.
Progressives said the clash with Mr. McConnell showed that Ms. Warren should run for president in 2020, while Republicans signaled that they were OK with her becoming the face of the party.
Later that month, the NRSC, the campaign arm for Senate Republicans, started running digital ads linking Ms. Warren to Democrats in 10 states.
They pointed out that Sen. Jon Tester received $10,000 from Ms. Warren’s political action committee — called PAC for a Level Playing Field — and that the Montana Democrat had voted with Ms. Warren 90 percent of the time, according to a Congressional Quarterly voting analysis of their records from 2013 to 2017.
Republicans also highlighted the voting similarities between Ms. Warren and Sens. Sherrod Brown of Ohio, 97 percent; Tammy Baldwin of Wisconsin, 96 percent; Claire McCaskill of Missouri, 88 percent; Heidi Heitkamp of North Dakota, 84 percent; and Joe Manchin III of West Virginia, 78 percent.
Each of those senators is up for re-election in states won last year by Mr. Trump.