The battle in Massachusetts between Sen. Scott Brown and Elizabeth Warren for U.S. Senate is locked in a dead heat, two polls released this week indicated.

One poll, from Western New England University, showed Warren edging Brown 50%-45%. Another survey, from WBUR, showed Brown with the advantage, netting the support of 47% of likely Massachusetts voters compared to 43% for Warren. Margins in both polls were within the sampling error.

The two candidates are waging a bitter fight in the state, with Brown raising questions about Warren's claims to Native American heritage and Warren volleying back, asserting Brown has ties to big banks on Wall Street.

The two last debated October 1. At that event, both candidates stuck to messages of independence from their respective parties, as well as the barbs they've used on the campaign trail and in television ads.

"I vote about 50 percent with my party and about 50 percent with the Democratic Party," Brown said at the debate, held at the University of Massachusetts-Lowell. "That's a lot different than what Professor Warren would do."

Sitting next to Brown at a table on stage, Warren took issue with the senator's self-portrayal as a bipartisan lawmaker.

Asked, however, whether she felt she could work with any current Republican members of the Senate, Warren named only retiring Sen. Dick Lugar of Indiana, who lost his seat in a heated primary battle earlier this year.

Pressed further, the Harvard law professor said it would "depend on the issue" and pointed to her experience "working across the aisle" when she served as Obama's adviser during the formation of the Consumer Financial Protection Bureau.

The Western New England poll released Monday surveyed 440 likely voters by telephone between September 28 and October 4, and the sampling error was plus or minus 4.7 percentage points. WBUR's poll surveyed 501 likely voters by telephone October 5-7, and the sampling error was plus or minus 4.4 percentage points.