But others were more critical of the cuts, including Rep. Raul Grijalva, an Arizona Democrat and co-chairman of the progressive caucus.
"Federal employees work every day to inspect our food, deliver Social Security checks and ensure our loved ones arrive safely at airports around the country," he said. "I strongly oppose a budget deal that asks federal employees to endure another pay cut."
The accord did little to placate leading conservative groups, who attacked the deal even before its details were announced.
"There's a real concern about giving up the sequester," said Sen. Orrin G. Hatch, a Utah Republican, who said he would be disinclined to back such a deal. "Republicans know that the one major victory they had was the sequester."
House Speaker John A. Boehner has faced a similar challenge in the past, when conservatives in his party rejected previous budget deals. If he can't count on a majority of Republicans, he would be forced to rely on Democrats for passage — something he has been reluctant to do because it dilutes his power.
Already, 30 House Republicans have signed a letter in support of keeping the sequester cuts, and GOP aides expect as many as 100 Democratic votes would be needed to secure passage because of likely GOP defections.
But as details of the deal emerged, it was unclear whether Boehner could pick up enough Democratic support.
Jim Dean, chairman of Democracy for America, said Democrats should reject the deal because it fails to include an unemployment insurance extension. "Negotiators have declared war on Christmas and potentially sentenced millions of struggling Americans to a very bleak New Year," he said.
In the Senate, even though Democrats have the majority, Senate Majority Leader Harry Reid would need a handful of Republican votes to overcome an expected tea party-led filibuster.
Pressure on Republican senators to oppose the deal was coming not only from conservative groups but from conservative candidates challenging incumbents in 2014 primary races.
Sen. Mitch McConnell, the Republican minority leader who is facing a primary attack in Kentucky, said Tuesday that the sequester law has been a "success, and I hope we don't revisit it."