Remember the Summer of 2010 and how the GOP held the Deficit Ceiling hostage? Here is an idea. Why don't the Democrats insist that all post 2001 tax cuts be repealed or they won't agree to raise the ceiling. Use the argument that the American people want tax increases on the wealthy to balance the budget.
Argue that the Sequestration was a good idea except that it was one sided and now to be fiscally responsible and protect popular government programs the Bush era tax cuts should be fully repealed. Simply refuse to raise the Debt Ceiling until the Republicans agree to be more responsible.