On Tuesday, voters in Rhode Island and Utah will go to the polls to vote in primaries for special elections that are set to happen in November. In Rhode Island, the Democratic primary is exposing fissures in the party’s left flank.

In the primary for Rhode Island’s special election in the first district, the campaigning between Democrats has become fierce as they vie to be the nominee, who will likely succeed Representative David Cicilline in the heavily Democratic district.

Of the 11 candidates seeking the Democratic nomination, a White House aide to Presidents Obama and Biden, Gabriel Amo, stands out for his connection to the highest executive office. Yet a state senator, Sandra Cano, the lieutenant governor, Sabina Matos, and a state representative, Aaron Regunberg, also have significant political experience and financial backing.

Mr. Regunberg went into the final stretch of the campaign with the largest war chest, at $630,000, followed by Mr. Amo with $604,000 and Ms. Matos with $558,000.

The race has become a point of division within the left wing of the Democratic Party, with Senator Sanders and Representative Alexandria Ocasio-Cortez backing Mr. Regunberg, while the local chapter of the Democratic Socialists of America issued a statement against the candidate.

In July, Mr. Sanders endorsed Mr. Regunberg, saying that “he understands the vital need to stand up against large corporations who have too much control over political and economic systems.”

“He supports Medicare For All because he knows Big Pharma and the health insurance industry continue to put their own greed ahead of the lives of thousands of Americans,” Mr. Sanders said. “At a time when we’re living with record high temperatures and devastating flooding, Aaron [also] understands that we can’t address catastrophic climate change without boldly taking on Big Oil.”

The endorsement was a boon for Mr. Regunberg’s campaign. With the candidates vying to to replace Mr. Cicilline, known for being one of the more left-leaning Democratic members, Mr. Sanders’s influence might have carried the race if the local DSA chapter had not stepped in.

“Providence DSA does not comment on every race, but the contrast between Regunberg’s rhetoric and actions is so stark that we feel the need to speak up,” the group said. “Whatever his intentions, Regunberg has a clear history of undermining progressives and collaborating with the pro-corporate Democratic Party establishment.”

While the Providence DSA is a fairly marginal group compared to Mr. Sanders, the oppositional rhetoric demonstrates a break between the grassroots and elected officials, which is mirrored in Mr. Sanders’s early endorsement of President Biden, despite Cornel West’s challenge from the left.

To further complicate matters, Ms. Matos is backed by the Hispanic Caucus, and Mr. Amo is backed by the Black Caucus, putting these three prominent parts of the Democratic coalition in competition with each other.

On the Republican side, a Middletown town councilwoman, Terri Flyn, will compete with a retired Marine who served in both Iraq and Afghanistan, Gerry Leonard. Given the district’s significant lean in favor of Democrats, either would be a long-shot candidate. The general special election will happen on November 7.

In Utah, Republicans will be competing to become the likely replacement for Representative Chris Stewart of the state’s Second District. The winner will compete with the Democratic nominee, Kathleen Riebe, a state senator who is the minority whip of her conference.

In the GOP race, attorney Celeste Maloy, a state representative, Becky Edwards, and businessman Bruce Hough will face off in a competition for the nomination in a district that leans heavily in favor of Republicans. In the past 20 years, Utah has sent to Washington only two representatives who were not a Republican.

Going into the competition, it looks like Ms. Edwards is favored to win the nomination, leading both in what little polling has been done as well as in fundraising.

In such special election primaries, though, low turnout can mean that a small group of voters can change the results of an election. According to the Salt Lake Tribune, between 100,000 and 200,000 people are expected to vote in the election, and it’s not clear voters have been paying too much attention to the race.

The single poll done for this election was performed by Deseret News and the Hinckley Institute of Politics, and it found that nearly half of GOP voters, 47 percent, were undecided on who they would support. 

Ms. Edwards was the leader of the pack, with 32 percent support. Mr. Hough was second with 11 percent, and Ms. Maloy was in third place, with 9 percent. The poll of 471 registered Republican voters in the district was performed in mid-August and had a margin of error of plus or minus 4.51 percent.

While neither election is expected to be a flip for either party, meaning they will likely not change the size of either conference in the House, the relative performance of each party in each race will be useful data points in taking the temperature of the national political climate.