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Michael Steel, spokesman for Mr. Boehner, says there’s a better movie analogy: “300,” the story of doomed Greek forces holding off invading hordes.

“We’re the Spartans trying to hold Thermopylae. The White House is the other Greeks - they say the right things but they aren’t actually very helpful. And the congressional Democrats are the Persian horde, desperately trying to cram more wasteful spending through the gap,” he said.

For now, though, the F-35 vote remains the only public test, and the vote breakdown showed just how difficult it is to cut big programs.

All 18 of Ohio’s representatives, from both parties, supported the $485 million in spending. The alternate engine is being developed in part at GE Aviation, based in Cincinnati.

Among Blue Dogs, the coalition of fiscally conservative Democrats, the vote was only marginally in favor of cutting. And even among progressives, who are generally seen as skeptical of big defense budgets, the vote was split with about three-fifths in favor of the cut and two-fifths opposed.

Many Democratic offices seemed reluctant to talk about their votes on the F-35 engine.

Rep. Dennis J. Kucinich, an Ohio Democrat and former presidential candidate who is on record calling for deep defense cuts and criticizing Pentagon waste, voted to preserve the spending. A spokesman didn’t return multiple messages seeking comment.

Neither did spokesmen for Reps. Maxine Waters and Lynn Woolsey, California Democrats who both voted “present” rather than take a stand on the amendment.

Rep. Louise M. Slaughter, New York Democrat, also voted present. Her spokesman said she saw good arguments on either side of the debate, and voted present because she knew her vote wouldn’t have changed the outcome.