SOUTH BOSTON—Voters trekked to the polls Tuesday morning to cast ballots in the party primaries that by tonight will narrow the field of serious contenders for the state’s U.S. Senate seat down to two.

On Monday, Secretary of State William F. Galvin, the state’s top election official, predicted that overall turnout would decline from 2009, the last time party primaries were held in preparation for a special senate election. On Tuesday morning, no signs had surfaced indicating Galvin’s prediction would be incorrect.

At the Foley Apartments on H Street in South Boston’s waterfront, Democratic candidate and U.S. Rep. Stephen F. Lynch cast his vote shortly after 8 a.m, accompanied by his wife, Margaret. Recent polls show that Lynch trails his opponent, the veteran U.S. Rep. Edward J. Markey of Malden, by about 10 points. Lynch said last week that his own polling shows the race to be much closer, and that he believes he will win.

Speaking to reporters after casting his ballot Tuesday morning, Lynch echoed that optimism, saying that he expected to prevail despite predictions of low turnout, which experts said would likely benefit Markey, the better-funded and more party-line candidate of the two.

“I’m not worried about South Boston, but I’m worried about some other areas that don’t know us as well,” Lynch told reporters. “But this is my third [special election], and we’ve sort of figured out how to work these things, and I expect to win tonight.”

Only about 50 voters had made their way to the Foley Apartments by the time Lynch cast his ballot on Tuesday morning, though poll workers said they expected activity to pick up later.

One morning voter, Bob Chisholm, a cab driver from Dorchester, told The Crimson he was supporting Lynch. He said he has friends who had worked in construction with Lynch, a former ironworker whom he deemed “our kind of guy.”

“I ain’t a Markey guy, that’s for sure,” Chisholm said. “I told all my friends to vote, too.”

Still, Chisholm acknowledged that his candidate faced an uphill battle.

“The thing that might hurt Lynch is his vote on Obamacare, but hey, he stood to his principles,” Chisholm said, referencing the candidate's vote against the Patient Protection and Affordable Care Act, the landmark 2010 health care bill championed by President Barack Obama.

The issue has generated contentious debate in a campaign that has otherwise kept a relatively low profile. Markey voted yes on the legislation, and has called that vote “the proudest of my career.”

Both parties are holding modified open primaries, which allow independent registered voters to vote in either, but not both, of the races. Three Republicans—former U.S. Attorney Michael J. Sullivan, former Navy SEAL Gabriel E. Gomez, and State Rep. Daniel B. Winslow—are competing in the Republican primary. The polls close at 8 p.m.

—Staff writer Matthew Q. Clarida can be reached at clarida@college.harvard.edu. Follow him on Twitter @MattClarida.