"All Obama has done for the last four years is clamor for higher taxes to spend more money," the president of Americans for Tax Reform told CNBC. "The only time we've beat him back on spending at all was during the debt-ceiling crisis."
Norquist said Obama was "willing to save $1 trillion by not occupying Iraq for the next decade. He wanted to count that like not continuing the War of 1812 was his budget cut."
He added that raising taxes isn't a compromise because the problem is spending.
(Read More: Geithner Warns US to Hit Debt Ceiling Monday)
He also called on the Senate to pass a budget, which it has failed to do for years. "Then we could compare it to the Republican budget and perhaps we could compromise on how much spending we need to bring down," Norquist said.
When we get past the cliff, any hike in the debt ceiling should be accompanied by similar cuts in spending, Norquist said.
(Read More: Why Congress Might Abandon the Debt Ceiling")
"[Speaker John] Boehner and Sen. Mitch McConnell have made clear if the president wants a dollar of debt-ceiling increase, we need to cut spending a dollar. That goes for $1 trillion," Norquist said. "That kind of spending restraint is exactly the kind of thing we need to do in the future for any debt-ceiling increase —period."