Volunteers for State Rep. Daniel B. Winslow, one of the three Republicans vying to represent Massachusetts in the U.S. Senate, work the phones on Tuesday afternoon. Winslow said that his volunteers made almost 200,000 calls during the campaign.

BOSTON—Campaign volunteers across the Commonwealth made thousands of last-minute phone calls on Tuesday afternoon, urging registered voters to turn out for the special election primary before the polls close at 8 p.m. Voters are choosing the two candidates who will face off in a June 25 special election to fill the U.S. Senate seat vacated when Secretary of State John F. Kerry was appointed to the Cabinet.

In the Republican race, public polls have showed former Navy SEAL Gabriel E. Gomez and former U.S. Attorney Michael J. Sullivan contending for the party’s nomination, with State Rep. Daniel B. Winslow in third. On Monday, though, officials with the Winslow campaign said that their internal polling showed the three men in a dead heat.

At Winslow’s downtown Boston headquarters on Tuesday afternoon, volunteers dialed frantically and kept receivers pressed to their ears, reminding supporters to make it to the polls and attempting to coax those on the fence to vote for Winslow.

“I was calling to see if you had a chance to vote today,” the refrain went, followed shortly by variations of “Any chance you voted for Dan Winslow?”

The frenzied phone drive was hardly a new scene at the campaign’s Milk Street headquarters, according to Winslow.

“The phones have been my campaign,” Winslow said in an interview on Tuesday afternoon. “We knew from the beginning that we weren’t going to be able to raise money like [Gomez], so we engaged in asymmetrical political warfare.... We targeted a very narrow bandwidth of people, Republicans and Independents, that we think will vote.”

The Gomez campaign took in more than three times as much money as the Winslow campaign, the Boston Globe reported. In this environment, Winslow Political Director Matthew Cocciardi said, the Winslow campaign had concentrated its limited resources on talking to likely voters either over the phone or in person, rather than on costly television advertising, which is harder to target.

“Essentially, we did a live touch of every voter who is going to be voting today and talked to them about Dan, where he stands on issues, and why they should support him,” Cocciardi said. “Gabriel Gomez went about it in a different way, with large ad buys, trying to target everybody and then trying to make sure they went and voted. We went right to the voters.”

Late Tuesday afternoon, Cocciardi said the strategy looked to be working. Though he predicted that turnout across the Commonwealth would come up short of expectations—Cocciardi estimated that only about 115,000 would vote in the Republican primary, while on Monday Massachusetts Secretary of State William F. Galvin anticipated as many as 200,000 voters—he said that reports from Winslow’s hometown of Norfolk, as well as surrounding areas, were encouraging.

“If you look at the numbers for us, Dan’s home district is coming out and voting,” Cocciardi said. adding that turnout also looked strong in Gomez’s hometown of Cohasset. In Plymouth, where Sullivan once served as district attorney, Cocciardi said it had been a slow morning, but that turnout had picked up in the afternoon.

“Right now, I think it’s anybody’s game,” Cocciardi said, noting that the Republican victor may not be known for hours after the polls close.

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