“Warren has been an outlier in her own party,’’ Cunningham said, referring to her hard-edged questioning of Obama administration officials in hearings on finance reform and consumer advocacy.

G. Calvin Mackenzie, professor of government at Colby College in Maine, pointed to ­Kennedy’s well-known ability to bring others on board.

“Ted Kennedy, for all the fire and brimstone liberalism, was also a guy who could sit down and deal; he could deal with Jesse Helms,” Mackenzie said.

In many respects, the difficulties both candidates could face in the Senate are a result of changes in Washington. ­Decades ago, there were Republicans who stood to the left of Democrats and Democrats who stood to the right of Republicans. Even those on the ends of the spectrum could negotiate without fear of losing their seat to a more ideologically pure replace­ment in a party primary.

The shift toward the modern brand of gridlock dates to the 1970s, when electoral reforms weakened the influence of party leaders, lending more influence to party activists, who were more ideologically driven, Mackenzie said.

Some of the best-known senators today are ideologues who work through the news media to gain a reputation as rhetorical leaders. Warren would face a choice if elected, whether to use her national popularity to become a leader of her party’s left flank or to work like Hillary Clinton did as a senator to ­become a student of the Senate.

Brown would also face a choice — whether to target his votes to build on his reputation for moderation, to work with other moderates to seek a more fundamental shift away from the Senate’s polarization, or to seek to build credibility with his party’s powers by leaning to his more conservative side.

Norman J. Ornstein, a political scientist at the American Enterprise Institute, said there is a sizable group of senators who may be willing to break out in the next session, to seek a more bipartisan path, if several more moderates win election Tuesday, as some polls project.

But Ornstein also believes that giving Republicans majority control would vindicate a GOP strategy of obstruction, designed to win back power by making the dysfunctional Senate the burial ground for Obama’s priorities. He blamed Brown for not standing up, during his two years in Washington, against procedural maneuvers meant to prevent the institution from even debating bills.

“The ability to judge Brown is a little bit more opaque, simply because he has voted with some of those filibusters,” said Ornstein, coauthor of “It’s Even Worse Than It Looks: How the American Constitutional System Collided With the New ­Politics of Extremism.”

The closeness of the race heading into the final two days underscores how torn some voters are ­between these competing visions of how the state should position itself in the ­national debate.

Tim Paikopolos, a 31-year old recent law school graduate from Dartmouth, stands at the fulcrum of that choice. He is a Democrat who says he plans to vote for President Obama against Mitt Romney, but he is undecided in the Senate race.

He fears Warren would fail to challenge her party or work with Republicans, ­because she has aligned herself so firmly with the Democratic base.

“Perhaps her independence would be compromised ­because she’s identified herself as strongly liberal or strongly Democratic,” he said.