"The president promised in the campaign sequestration would not happen. Now, he is allowing it to happen," Graham said on "Fox News Sunday."
"He's the commander-in-chief and on his watch, we're going to begin to unravel the finest military in the history of the world, at a time when we need it most," Graham, a member of the Armed Services Committee added. "If you want to look at ways to find $1.2 trillion in savings over the next decade, let's look at Obamacare. Let's don't destroy the military and just cut blindly across the board. There are many ways to do this."
However, Graham offered no specifics.
The Democrats propose generating revenue from plugging some tax loopholes. Those include tax breaks for the oil and gas industry and businesses that have sent jobs overseas and taxing millionaires at a rate of at least 30 percent.
Rep. Paul Ryan, who chairs the Budget Committee, advocates for plugging loopholes, but as part of a discussion on tax reform, not sequestration.
"Loopholes are necessary for tax reform," Ryan said on ABC's "This Week." ''If you take them for spending, you're blocking tax reform and you're really not getting the deficit under control."
With the March 1 deadline fast approaching, Sen. Chuck Schumer, a New York Democrat and close ally of the White House, predicted that Republicans will eventually join Democrats to avoid the cuts.
"They have no choice," Schumer said on CNN's "State of the Union." ''Their arguments are untenable and don't meet the favor of hardly anyone other than themselves and the special interests they're protecting."