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The type of real, red-faced debate that delighted Mr. Hatch and Kennedy also produced landmark laws like the Americans With Disabilities Act and children’s health insurance. With former Democratic Sen. Christopher J. Dodd, the bellowing begat federally subsidized child care. Tense talks with no less a partisan than Rep. Henry A. Waxman, California Democrat, produced a patent exemption that cleared the way for the generic drug industry.

Mr. Hatch’s last two years of ideological purity — a 100 percent rating from the American Conservative Union, compared with an average 84 percent rating the previous five years — may have been driven by a survival instinct, but it still irritates some.

Vice President Joseph R. Biden recalled how the Utah Republican was an original co-sponsor of his 1994 bill that became the Violence Against Women Act, only to vote against its renewal and expansion this year.

Orrin and I always had a good personal relationship. We disagreed on a lot, but where we found common ground, we worked together,” Mr. Biden said in a statement to the Associated Press. “I hope those days return.”

Tax reform could well be Mr. Hatch’s enduring legacy. The contours of the debate are clear and broadly philosophical: Republicans think the government levies enough taxes already but growing the economy would produce more revenue. Democrats say the wealthiest are not taxed enough.

Much, of course, depends on who wins the White House and control of Congress.