According to the Western New England University Polling Institute survey, Markey holds 44 percent support to Lynch's 34 percent support among likely Democratic primary voters, with 21 percent of voters undecided. 

The poll was conducted from April 11-18. Even two weeks out from the primary, a full 36 percent of likely Democratic primary voters said they could still change their mind about their vote. Sixty-four percent said they were very sure of who they're supporting.

Lynch posts a slight lead among voters unaffiliated with any party, taking 41 percent support from those voters, to Markey's 35 percent support. Though he has a difficult path to the nomination, it likely goes straight through that bloc, which makes up about half of Massachusetts' electorate.

Lynch's challenge is to turn out those unaffiliated voters in high enough numbers to overcome Markey's substantial lead among likely Democratic primary voters.

The poll follows a spate of good news for Markey, who received the Boston Globe's endorsement on the weekend and tripled Lynch in fundraising.

Markey brought in $4.8 million to Lynch's $1.5 million in the first four months of the year, and has $4.6 million cash on hand to Lynch's $514,000.

The two candidates have rescheduled a televised debate that was postponed last Thursday because of the Boston Marathon bombing. The debate will now be held on Tuesday. After pausing their campaigns last week following the bombing, Lynch and Markey both returned to the hustings over the weekend.

The state of the race is less clear among Republican primary candidates. Boston businessman Gabriel Gomez leads the GOP pack with 33 percent support among likely Republican primary voters, according to the Western New England University poll. Attorney Michael Sullivan, a former official in George W. Bush's administration, now takes 27 percent support. State Rep. Dan Winslow (R), received 9 percent support in the poll. 

Many in Massachusetts considered Gomez's campaign dead in the water following the release of a letter he wrote to Gov. Deval Patrick (D) asking to be appointed to the Senate seat shortly after Secretary of State John KerryJohn Forbes KerryNorth Korea is moved by Pompeo diplomacy, but Dems dig in deeper Ex-Obama official Marie Harf, Guy Benson to co-host Fox News Radio show Five things to know about Russian oligarch Oleg Deripaska MORE resigned.

In the letter, Gomez pledged his support for President Obama's agenda. Sullivan has attacked Gomez as an "Obama Republican" in one ad. 

But Gomez seems to have rebounded from any negative publicity generated by the letter, likely due in part to his prominence in the state following last week's marathon bombings. 

Gomez, a former Navy SEAL, ran in the race and finished shortly before the bombs exploded. He did a round of media interviews discussing his experience in the days following the attack.

Gomez also has the endorsement of former Gov. Bill Weld (R) and has built a substantial lead in fundraising — buoyed by a $600,000 loan of his own funds to his campaign.  

Looking towards a general election fight, Lynch performs better than Markey against every Republican challenger, although both lead all three GOP candidates by double-digit margins. 

The Western New England University poll was conducted among 480 Massachusetts likely voters from April 11-18, and has a margin of error of plus or minus 4.5 percentage points.