In the WBUR/MassINC Polling Group survey, Markey gets 38 percent of likely Democratic primary voters, while Lynch takes 31 percent. About a fifth of respondents didn't know who they would vote for or declined to answer the question.

Markey fares even better with Democrats alone, taking 42 percent support to Lynch's 25 percent support.

But Massachusetts' voting population is made up of about 52 percent "unenrolled" voters, who register with no party and can vote in either primary.

And among those unenrolled voters, Lynch has a slight lead, with 38 percent to Markey's 34 percent.

That indicates if Lynch hopes to be successful, he'll have to get those unenrolled voters to the polls, a difficult task in an odd-year primary.

Lynch and Markey fare about equally against a generic Republican opponent, taking just under 40 percent support, with a little more than a third of voters unsure or declining to answer the question. The race is still early, and Republicans only finalized their likely slate of contenders on Thursday, when the final two potential candidates announced their decisions.

Local businessman Gabriel Gomez, state Rep. Dan Winslow, former U.S. Attorney Michael Sullivan and local politician Jon Fetherston have all announced their intentions to run for the Republican nomination, and are currently working to get the 10,000 signatures needed to get on the ballot.

The survey tested Gomez, Winslow and state Sen. Bruce Tarr, who announced Thursday night he will not be running for the nomination. In all three cases, about a quarter of voters said they had heard of the candidates but hadn't made up their minds on them, and more than 50 percent of respondents said they didn't know the names. 

The survey was conducted among 498 registered voters from Feb. 11-13 and has a margin of error of plus or minus 4.4 percentage points.