President Obama's top economic adviser, Gene Sperling, said Sunday that while the sequester originated in the White House, Republicans are the ones who made sure it included only spending cuts and no revenue increases.

"I think it's most accurate that [Republicans] did propose an all-spending cut mechanism that would have this type of harmful impacts (sic) on defense and spending and on education and research," Sperling said during an interview on NBC's "Meet the Press."

Republicans have noted repeatedly that the sequester was Obama's idea, making it a centerpiece of their argument that he bears more blame for the cuts, which are now set to be instituted. They have cited the reporting of the Washington Post's Bob Woodward to make that case.

Presented with Obama's claim at a debate in October that the sequester originated in Congress, Sperling didn't back down. He borrowed an analogy from New York magazine columnist Jonathan Chait, who compared the sequester to a mugger asking for someone's wallet and that person volunteering to give them their watch instead.

"Well, technically, giving your watch was your idea, but it doesn't really tell the whole story," Sperling said.

He said Obama wanted a sequester that included revenue increases, but that Republicans and House Speaker John Boehner (R-Ohio) insisted that it contain all spending cuts.

Pushed further, Sperling emphasized that both parties supported the idea.

"The right answer is that we all did agree to this, and we all agreed to it to force us to compromise on long-term entitlements and revenue," Sperling said.