Karl Rove proposes a similar idea.
One of the problems with the sequester -- which this proposal would attempt to address -- is that its spending cuts come uniformly, from almost every government account. That's why they're often called indiscriminate and across-the-board. Under the sequester it doesn't matter if one part of an agency is bloated and another part is lean: both must be cut.
The GOP proposal would give the executive branch more discretion over where to make those cuts for the remainder of the current fiscal year, which ends in September. After that date, congressional appropriators would make decisions about where the specific cuts would come from, while still adhering to the sequester's new lower spending baseline.
The irony is that in the near term, the GOP's proposed fix would delegate a great deal of authority to the executive branch -- and thus to President Obama. And for the GOP that would come with the risk that the administration would target the cuts at GOP constituencies, which would undermine the political rationale for their own plan.
But aside from that potential flaw it's a clever idea. In effect, it's a sequester replacement bill minus the political cost of proposing specific alternative cuts to federal programs. It would set a new, lower baseline for spending at the executive departments, including defense, and leave it to bureaucrats, or future congressional leaders, to determine which programs are high priority and which are not. It would still constitute significant austerity -- $85 billion in cuts over the next several months -- but would lead to a substantively better outcome than if President Obama were forced to order the sequester in its current form.
Thus it comes with the added benefit for Republicans of putting Democrats in an awkward spot. They'll be forced to decide whether to support a plan that partially defangs the sequester by making its impact much less arbitrary, but that simultaneously violates their demand that the sequester be replaced with both alternative spending cuts and new tax revenues.
Senate Democrats expect Republicans to offer up a plan like this as an alternative to their own sequester replacement bill, and are poised to vote it down, according to a senior Democratic aide. That's probably where the story ends. House Republicans would have a hard time passing a plan like this on their own, and even if they did, Senate Dems would have already rejected it. But it'll provide Republicans some cover once the sequester hits and pressure grows on them to cave on taxes.