For the last week, all I've heard about is that the new plan for the Republicans is to let the sequester take effect.
But thinking about the sequester ($85B in cuts taking effect March 1 unless Congress does something) by itself makes no sense, and there's a pretty good chance that everyone in Congress (and the Oval Office) knows it. Because right after the sequester hits, on March 27, current funding for the government expires and a new Continuing Resolution will have to be passed. Given that the CR sets spending totals for the remainder of the year, it will -- not can, but will -- replace the sequester. Now, appropriators may choose to act differently based on what current policy might be (in other words, whether the sequester goes through as planned, is replaced, or is cancelled altogether). But there's no particularly reason that they have to accept whatever happens on March 1. That's especially true for the discretionary portion of the sequester, but it's pretty much also the case for the rest of it, too.
Of course, any cuts that are there for just a short while can still be quite disruptive, even if it's just four weeks. Still, that's almost certainly something most politicians would accept if it gets them out of a tough vote. As far as its effect on the CR: on the one hand, "locking" in the lower spending levels on everything might make it harder to secure some GOP votes than if the sequester had never bit. On the other, however, letting the sequester happen could allow Members of Congress to get to be heroes for restoring whatever gets cut on March 1.
It's also certainly possible that the CR deadline ends with a government shutdown while everyone negotiates a deal they can all live with. And it's also possible that what we'll see at the end of this month is movement towards aligning the two deadlines, since it really doesn't make much sense to hold two such fights four weeks apart (although of course if they did strike a deal to replace the sequester by March 1 it could easily be packaged with early passage of the CR).
At any rate: there's nothing magic about the sequester. It happens or doesn't happen, and then Congress does whatever they're going to do next, and nothing in the sequester binds Congress from replacing it.