The three-month sprint to the special election Senate primary in Massachusetts is expected to be expensive and draw multiple Members of the Congressional delegation — many of whom have been dreaming of running statewide since the Bay State last had an open Senate seat in 1984.

The death of Sen. Edward Kennedy (D-Mass.) has left big shoes to fill, but for Democratic Members of the state’s delegation eyeing the abbreviated race, more is not always merrier. Having several Boston-area Democrats run for the seat — including Reps. Mike Capuano, Stephen Lynch and Ed Markey — could put Attorney General Martha Coakley (D) in a good position to win the Dec. 8 primary, strategists say.

Coakley is the only Democrat officially in the race but won’t likely be the last to throw her hat into the ring. Capuano and Lynch have already picked up the appropriate paperwork to file for the special.

In a Wednesday phone interview, Coakley acknowledged that her campaign started at “zero— compared to the fundraising of some of her potential competitors. She said she will need to raise at least $2 million to be competitive in the special election, and her campaign could cost up to $6 million.

“We believe we have commitments by Sept. 30 to have at least $1 million on hand,— Coakley said.

Depending on which Bay State Members get into the race, she could be facing fellow Democrats who already have almost $3 million stockpiled in their campaign bank accounts — valuable funds in a short-sprint special election. Coakley was in Washington, D.C., on Wednesday, where she was endorsed by EMILY’s List in the Senate race.

“We are already up and running,— Coakley said. “We’ve got statewide recognition. We’ve got boots on the ground already collecting signatures. Those are costs that they’re going to have to incur.—

But according to former Massachusetts Democratic Party Chairman Phil Johnston, Bay State party officials and activists are waiting to see what Markey decides about the race. Markey reported having $2.89 million in his campaign account at the end of June.

“If Ed Markey runs, it’s going to make it even more interesting because he’s the dean of the delegation,— Johnston said. “He’s currently one of the most powerful people in Washington.—

According to a source close to Markey, the 18-term Democrat was still thinking about a bid Wednesday night.

“The Congressman is still weighing his options and will be making a decision in the near future,— the source said.

The three House districts represented by Lynch, Capuano and Markey border each other and include most of the Boston metropolitan area. If all three Members run in the Democratic primary, they could cut into each other’s base and open the race for Coakley.

Markey’s “district adjoins Mike Capuano’s district and one could argue that they pull from somewhat of the same base, so the question would be whether or not they cut into each other in ways that could help Martha Coakley or Steve Lynch or any of the other opponents,— Johnston said.

In an effort to distance himself from the pack, Lynch, the only anti-abortion candidate in the race, will likely present himself as a moderate Democrat.

Capuano has already indicated that he will run to the left of the field. When he picked up the appropriate paperwork earlier this week to run, Capuano evoked Kennedy’s “progressive ideals— in a statement and said he thought he was the best candidate to follow in those footsteps.

While Capuano and Markey have similar liberal political profiles, Markey would have an advantage because he can talk up his role in recent energy and health care reform legislation as chairman of the Energy Independence and Global Warming Committee — a key talking point with liberal activists who are more likely to turn out to vote in a special election.

Rep. John Tierney (D-Mass.) is the least likely to get in the race, but he has yet to rule out running. His spokeswoman declined to comment on a bid. Another Democrat, City Year co-founder Alan Khazei, is also talked about as a poten tial candidate, but he would have serious hurdles to overcome to defeat the elected officials.

But Markey and Lynch, both of whom came to Congress by winning special elections, might be the first to point out that this contest will be its own beast. The special election primary will likely have low turnout because of the holiday season, and it’s likely the liberal activists and elderly could dominate the electorate.

And with Democratic juggernauts such as former Reps. Joe Kennedy and Marty Meehan taking themselves out of the race, the competition between Coakley and the Democratic Members only increased.

Meehan stepped down from his 5th district perch in 2007 to become chancellor at the University of Massachusetts at Lowell. With almost $5 million left in his account, the 52-year-old former Member said Tuesday that he was not going to run for Senate but left the door open to running for public office again.

“I’m not ruling out the possibility of seeking public office in the future,— Meehan said in a Wednesday phone interview. “I will use that money, if and when, I seek public office at some point in the future. One of the reasons I believe I could have won is because I could have financed that race.—

Senate Republicans are not optimistic about winning the Senate seat, although several potential GOP candidates have made noise about the bid. Former White House Chief of Staff Andrew Card is considering running, plus state Sen. Scott Brown is expected to announce his intention to get into the race soon. Former Red Sox pitcher Curt Schilling has openly discussed a bid on his blog but has made clear that he is unlikely to run for the seat.

In the meantime, Bay State legislators are working on changing state law so that Gov. Deval Patrick (D) can appoint an interim Senator until the special election is complete. Following Kennedy’s death, Senate Democrats are one vote short of the filibuster-proof majority to pass legislation.