Washington Examiner gives, from a conservative's standpoint, a somewhat more nuanced opinion on the pickle Republicans find themselves in:

In a Wall Street Journal op-ed Wednesday, House Speaker John Boehner describes the upcoming sequester as a policy “that threatens U.S. national security, thousands of jobs and more.”

Which leads to the question: Why would Republicans support a measure that threatens national security and thousands of jobs? Boehner and the GOP are determined to allow the $1.2 trillion sequester go into effect unless President Obama and Democrats agree to replacement cuts, of an equal amount, that target entitlement spending. If that doesn’t happen — and it seems entirely unlikely — the sequester goes into effect, with the GOP’s blessing.
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Could the GOP message on the sequester be any more self-defeating? Boehner could argue that the sequester cuts are necessary as a first — and somewhat modest — step toward controlling the deficits that threaten the economy. Instead, he describes them as a threat to national security and jobs that he nevertheless supports. It’s not an argument that is likely to persuade millions of Americans.

The GOP’s astonishingly bad message on sequester cuts