BOSTON (CBS) — In past elections, the Massachusetts primary has been something of an afterthought. But with Bernie Sanders campaigning hard here in an effort to knock out Elizabeth Warren on her home turf, the result here will be closely watched on Tuesday night.

With just two days to go before voting day, Sanders and Warren are in a virtual tie in a new Suffolk University/WBZ/Boston Globe poll, with the Vermont senator holding a narrow lead well within the survey’s 4.4% margin of error.

In a bit of a surprise, Michael Bloomberg sits in third place, just a fraction ahead of Pete Buttigieg. Joe Biden places fifth, but those three are all within the margin of error.

READ MORE: MASS. TRACKING POLL | CROSSTABS

While the poll shows Warren within reach of a win here, the question remains: why isn’t she doing better in her home state? A deep dive into our survey reveals some troubling answers for the Warren campaign.

Among female voters, Warren leads with 29%, but Sanders is right behind her with 25% — again, well within the poll’s margin of error. And look who’s tied for third with Buttigieg: Bloomberg, who’s been under attack from Warren for his past interactions with women who work for him.

Another eyebrow-raiser — Sanders and Bloomberg are tied among a crucial voter group, independent or unenrolled voters, with 21% each. Warren trails in third place with just 16%, a sign of failure to appeal beyond her liberal base.

Our poll offers some cautionary signs for Sanders as well. His support here relies heavily on voters aged 18 to 35, beating Warren among them by nearly two-to-one. But he craters among older voters, finishing a distant fifth with 55 to 65-year-olds.

And finally, the poll includes a warning for the Democrats: 15% of voters overall, and a stunning 30% of independents say if the party doesn’t choose their preferred nominee, they’d vote for President Trump or a third-party candidate in November.

Our next Suffolk University/WBZ/Boston Globe poll will be released Sunday at 6:30 p.m. This time, we’ll be monitoring the Democratic U.S. Senate primary race between incumbent Ed Markey and challenger Joe Kennedy.