There are a lot of stories running around with titles like "McConnell Caves" and "McConnell's Retreat". They're all talking about the fallback plan floated by Senate Minority Leader Mitch McConnell (R-KY). That plan, if passed by Congress, would allow President Obama to raise the debt limit in three stages. Each debt ceiling increase would be required to be accompanied by spending cuts of the same size.
This plan has already gotten approving comments from Senate Majority Leader Harry Reid (D-NV) House Minority Leader Nancy Pelosi (D-CA), and Arizona Senator John McCain. None of these approvals is likely to gain much additional Republican support for the plan.
I wonder if there isn't something else involved in this gambit. If Obama and the Congressional Democrats accept McConnell's plan, they commit to spending cuts equal in size to each of the three debt ceiling raises but there are no tax increases. Thus, under this plan, the spending cuts come but Obama's obsession with raising taxes fails. And the chances of the House passing this plan after that are very small.