Christine Todd Whitman gives Brown the thumbs-up at Phillips Old Colony House: The former New Jersey governor, left, joined Sen. Brown at the landmark Morrissey Boulevard eatery and function hallon Tuesday afternoon.

U.S. Sen. Scott Brown on Tuesday picked up the endorsement of former New Jersey Gov. Christine Todd Whitman in Dorchester.

Looking for a full six-year term, Brown, a Wrentham Republican, is in a close battle with Democratic candidate Elizabeth Warren. A WBUR poll released Monday showed Brown up by four points.

“You vote for the person,” Whitman told reporters, standing next to Brown at the Phillips Old Colony House on Morrissey Blvd.

Whitman, who studied at Wheaton College in Norton, Mass., served as governor of New Jersey from 1994 to 2001, according to a biography on her consulting firm’s website. She also served as President George W. Bush’s Environmental Protection Agency chief.

In a media advisory touting the endorsement, Brown’s camp noted that Whitman was a “fiscal conservative and social moderate, and an outspoken advocate of a big tent Republican Party.”

Asked whether she was voting for former Mass. Gov. Mitt Romney for president, Whitman did not provide a direct answer, citing “the beauty of an independent" and private ballot.

Last year, Whitman told POLITICO that she was urging then-Republican presidential candidate Jon Huntsman, a Romney rival, to mount an independent bid for the White House.

Brown, who shares some advisers with the Romney camp, pointed to Republicans who are fiscally conservative and socially moderate, a shrinking caucus.

Brown rattled off the names of Richard Lugar, Joe Lieberman, Kent Conrad and Olympia Snowe, all considered centrist Democratic and Republican senators who will not be returning to Capitol Hill next year. “We’re a dwindling breed,” he said.

After the press conference, Whitman and Brown, along with Brown’s wife, Gail Huff, headed to the back of the Phillips House for a private luncheon.