So long as the Senate refuses to deal with any budget passed by the House, we remain on the Baseline Budgeting Autopilot — the departments get last year’s budget plus X or Y%.”
This sounds like poppycock. If there ain’t a continuing resolution approved by the House things shut down!!! i.e. Newt Gingrich shut down in 1995-6!!
It's not poppycock. They can vote to fund something or de-fund something else -- but it has no effect unless the Senate agrees.
A continuing resolution is, in fact, now the only control that the House has over total spending. They don't necessarily have any control over individual elements of the spending.
Which is to say, that the only lever they have IS to shut the government down. And they've repeatedly said they wouldn't do that.
I would remind you that Congress has not passed a budget since FY 2009. All budgets since have been a product of the previous year's Current Services Baseline, plus an arbitrary escalator.