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For his part, Mr. Norquist said Mr. Boehner, Ohio Republican, and Mr. Cantor support stronger economic growth, not tax increases.

Asked Monday during an appearance on MSNBC’s “Morning Joe” whether he still stands by the pledge, Mr. Cantor ducked. “There’s a lot that has been said about this pledge, and I will tell you when I go to the constituents that have elected, re-elected me, it is not about that pledge. It really is about trying to solve problems,” Mr. Cantor said.

The remarks came a week after Mr. Chambliss told a Georgia television station, “I care more about my country than I do about a 20-year-old pledge.”

Mr. Graham and Mr. King also broke with Mr. Norquist over the weekend.

“I agree entirely with Saxby Chambliss,” Mr. King said. “A pledge you signed 20 years ago, 18 years ago, is for that Congress. For instance, if I were in Congress in 1941, I would have signed the — I was for the declaration of war against Japan. I’m not going to attack Japan today. The world has changed, and the economic situation is different.”

Mr. Norquist countered that the pledge covers a lawmaker’s entire time in Congress.