(CNN) - The clock is ticking for the GOP in Massachusetts.
With Election Day just four and a half months away, Republicans have yet to find a candidate to run in a special contest to fill the final eighteen months of the term of longtime Democratic Sen. John Kerry, who stepped down from the Senate Friday to succeed Hillary Clinton as U.S. secretary of state.
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Monday former Republican Gov. William Weld, who was elected twice in the 1990's as Bay State governor, announced he would not make a bid.
"While I am grateful for the kind expressions of support and encouragement which I have received, I will not be a candidate for United States Senator from Massachusetts in the special election this year," said Weld said in a statement released by the law firm where he is employed.
Weld moved from New York back to Boston recently, and there was some speculation that he might make a second run for the Senate. Weld's unsuccessfully challenged Kerry in 1996.
Weld is the third Republican to say no to a Senate bid over the past couple of days. On Saturday former state Senate Minority Leader Richard Tisei said he would sit out the election. In November Tisei nearly ousted Democratic Rep. John Tierney in Massachusetts' 6th Congressional District.
And on Friday, the candidate Bay State Republicans had hoped would run, former Sen. Scott Brown, also said no.
In January 2010, then state lawmaker Brown upset Democratic candidate Martha Coakley, the state's attorney general, in a special election to fill the final two years of the term of longtime Democratic Sen. Ted Kennedy, who died the previous summer.
Brown won the special election by five points over Coakley, but lost his re-election bid in November to Democratic challenger Elizabeth Warren by eight points. Around 2.3 million voters cast ballots in the 2010 special election, and nearly 3.2 million voted in last November's general election.
"Over these past few weeks I have given serious thought about the possibility of running again, as events have created another vacancy requiring another special election. I have received a lot of encouragement from friends and supporters to become a candidate, and my competitive instincts were leading in the same direction," said Brown, in a statement.
But he added that "even so, I was not at all certain that a third Senate campaign in less than four years, and the prospect of returning to a Congress even more partisan than the one I left, was really the best way for me to continue in public service at this time."
So who's left?
The Boston Herald reported Monday that former Massachusetts Gov. and 2012 GOP presidential nominee Mitt Romney's 42-year old son Tagg is considering a run.
But a source close to the Romney family told CNN that Tagg is "thinking about it, but it's unlikely."
The source asked for anonymity to speak to more freely, as did a GOP strategist in Massachusetts who also didn't put a lot of stock in Tagg Romney running.
Tagg, who started the venture capital firm Solamere Capital after his father's 2008 bid for the GOP nomination, advised his father in both that bid and in the 2012 presidential campaign. Mitt Romney lost his home state by 23 points to President Barack Obama in last November's election.
Other names that come up in connection with the Senate campaign: Former Lt. Gov. Kerry Healey, Gabriel Gomez, a former Navy Seal who works in the finance industry, and state Rep. Dan Winslow, who says he'll announce Tuesday whether he'll launch a campaign. Winslow served as chief legal counsel for then Gov. Romney.
Whoever runs will need to gather 10,000 signatures in the next three and a half weeks to qualify for the ballot. If there is more than one GOP candidate, they would square off on primary day, April 30.
At least two Democrats will face off that day in their party's primary.
Thursday Democratic Rep. Stephen Lynch announced his bid for Kerry's Senate seat, becoming the second candidate to jump into the special election. Lynch joins fellow Democratic Rep. Ed Markey, the longest serving member of the Bay State's congressional delegation.
Wednesday Democratic Gov. Deval Patrick announced that a trusted former aide was his choice to serve as an interim replacement for Kerry. Patrick named William "Mo" Cowan, his former chief of staff, as senator.
Cowan, who will serve through the June special election, will become the second African-American in the U.S. Senate, alongside Republican Tim Scott of South Carolina. Scott, who was just elected in November to a second term as a congressman, was named last month to succeed Sen. Jim DeMint, who stepped down from his seat.
CNN's Jill Chappell contributed to this report