After he emerged as a political sensation following his victory in the 2010 special election, Brown repeatedly registered in polls as the most popular political figure in the state. And while he remains well liked, with 54 percent of respondents viewing him favorably and 29 percent unfavorably, he now passes the mantle of most-popular to an unexpected successor: Attorney General Martha Coakley, the Democrat who was ridiculed nationally after her defeat to Brown in that special election.

“This is a wide open race,’’ said Andrew E. Smith, the director of the University of New Hampshire’s Survey Center, which conducted the poll. “Both candidates are generally well liked. Unless something dramatic happens, this will go down to the wire.’’

Still, roughly a third of voters in those two groups remain undecided, according to the poll, and whichever candidate wins them over will be in a strong position come November.

Both candidates appear to be faring well among the voting blocs each needs most: Brown outpaces Warren by three to one among self-described independents, voters Republicans depend upon in this heavily Democratic state. Warren holds a better than three-to-one lead among those who identify themselves as conservative and moderate Democrats, a group of voters who helped form Brown’s coalition two years ago, when he first won office.

With a long seven months to go before Election Day, the survey shows Brown with 37 percent of the vote and Warren with 35 percent, while 26 percent said they are undecided. That amounts to a statistical tie, as the telephone poll of 544 randomly selected likely voters, taken March 21-27, has a margin of error of plus or minus 4.2 percentage points.

Few poll respondents associated her with the “Harvard elitist’’ label that Brown has tried to tag her with. Likewise, only one in five of those surveyed agree with Warren’s argument that Brown is marching in lockstep with the Republicans.

Voters seem to have responded to Brown’s message that he is a moderate, independent, and likable political figure, looking out for the state’s interest regardless of party. And Warren, though less known, is seen by many as a consumer advocate, who would champion working people, tax the rich, and battle corporations.

The survey found that both candidates remain popular and are successfully managing their core political message and fending off attacks on their public image at this early stage of the campaign, which has become a focal point for the national parties as they vie for control of the Senate.

Republican Senator Scott Brown and Elizabeth Warren, his likely Democratic opponent, are locked in a dead heat, with a large bloc of voters still undecided about which candidate to back in this marquee matchup, a Boston Globe poll has found.

Coakley, who easily won reelection and has quietly rebuilt her reputation through her work as attorney general, is now viewed favorably by 62 percent of voters, and unfavorably by 23 percent, according to the poll.

Governor Deval Patrick, who just over two years ago was being consigned by Democratic supporters to the political graveyard, has continued to see his popularity rise. He now is slightly more popular than Brown, with 57 percent viewing him favorably and 27 percent unfavorably.

His deputy has not fared nearly as well. Lieutenant Governor Timothy P. Murray, who has been dogged by questions about an early-morning car crash that totaled a state car and also about his associations with a former Chelsea housing official under investigation for corruption, has seen his favorability drop to 29 percent, while 30 percent view him unfavorably.

President Obama remains popular in Massachusetts, a state he carried easily in 2008 and one that has long been considered safe ground for Democrats in presidential elections, the poll found. Nearly three in five people view him favorably, his highest mark in the state since at least 2010.

That’s a contrast to former Governor Mitt Romney, the front-runner in the Republican primary, who is viewed unfavorably by more respondents - 47 percent - than favorably - 42 percent.

In a head-to-head matchup, Obama holds a 49 percent to 33 percent edge over Romney, with 16 percent of respondents saying they have yet to decide.

Those figures reinforce the prevailing wisdom that Massachusetts will not be a battleground state in the presidential contest, despite Romney’s ties here.

But both parties see the US Senate race as one of a handful in the country that will determine who will control the sharply divided chamber. Warren’s entrance into the race last fall kicked up huge excitement among Democrats, both in Massachusetts and across the country, giving them hope that the seat that was held by the late Edward M. Kennedy could be recaptured.

Most Democrats in the race soon dropped out. Warren’s lone remaining competitor in the Democratic primary, Marisa DeFranco, a North Shore immigration lawyer, is not known by 82 percent of those surveyed.

Warren is setting her sights directly on Brown, who is showing that he is anything but an easy target.

In one area that could prove significant as the race moves forward, Brown has a clear lead. Brown was viewed as more likable than Warren by 57 percent of voters, compared with 23 percent who said she was the more likable candidate. Even a plurality of Democrats said Brown was more likable.