A Businessweek article says that Republicans want cuts in Social Security's Cost of Living Adjustment (COLA),the chained CPI proposal, as their price for extending the debt ceiling.
I'd love to see Republican members of Congress go on record as favoring chained CPI but my opinion is that virtually none of them would vote for it. Republican members of Congress love to talk in the abstract about cutting the budget, particularly "entitlements", but are afraid of voting for any specific cuts in the budget, particularly cuts in Social Security and Medicare, the biggest entitlements. Voters are all for cuts in the budget and in "entitlements" in the abstract. They just don't favor specific cuts, especially cuts in Social Security and Medicare. That's how we end up with sequestration, which applies a simple percentage reduction to most government programs. The damage from this approach isn't as immediately obvious to the public.