“I’m giving it serious consideration, but there are a lot of challenging factors in this situation, not the least of which is the compressed time frame to be able to get 10,000 certified signatures, which regardless of someone’s interest in the race would make anyone have pause before moving forward," he told the State House News Service.

Tarr is one of a handful of state legislators proposed by Massachusetts Republicans for the seat. One other, state Rep. Dan Winslow, announced on Tuesday he is looking into a bid. Assistant Senate Minority Leader Robert Hedlund, as well as Worcester Sheriff Lew Evangelidis and local businessman Gabriel Gomez, have all been suggested as possible contenders.

Tarr said he would decide whether to launch a campaign by Monday at the latest. But he took a moment in speaking with the State House News Service to set up what could be attacks on his potential Democratic challengers, Reps. Edward MarkeyEdward (Ed) John MarkeyDemocrats protest Trump's immigration policy from Senate floor Dems press EPA nominees on ethics, climate Lawmakers prep for coming wave of self-driving cars MORE and Stephen Lynch.

"We have two people that have a long history in Washington that are in the race, in terms of the Democrats, and I think that clearly there’s something to be said for sending somebody to Washington that won’t perpetuate the gridlock," he said.

And he said, in offering his justification for considering a run, that he has made "strong efforts to find common ground."

"There is a model in this building that I think could well be followed in other places around the country, certainly inside the Beltway is one of them," he said.

Tarr gives the Massachusetts Republican Party one more potential option, after former Sen. Scott Brown's (R ), long considered the most viable contender for a special election in blue Massachusetts that looks tough by any metrics, announced he would not run on Friday.

A handful of other second-tier candidates dropped out in the following days: Former Gov. Bill Weld, former House GOP contender Richard Tisei and former Lt. Gov. Kerry Healey all announced by Monday evening they weren't interested in a run.