One thing we know about government employees is that they overwhelmingly vote Democratic. They do this for reasons of enlightened self-interest; Democrats spend more on government than do Republicans.
Democrats spend more in raises for government workers, increases in government worker retirement payments, and new or enlarged government programs which create employment and/or promotion opportunities for government workers. Republicans don't.
What is the sequester? A cut in government spending. Who is directly hurt by the sequester? Government employees, which is to say mostly Democrats. Is this a reason for Republicans to allow the sequester to take place? It could be.
Is it a reason for Democrat legislators to cave in and give Republicans what they want in return for legislation to forestall the sequester? It certainly could be just that. See this RealClearPolitics article for details.