There is no double negative per se. The sentence has a series of nested modifying phrases that build on each other in a way that is difficult to track. In addition, the interaction of the words disagree and debunk seems to create a semantic reversal:
- Starting with the simple unmodified subject and and the simple unmodified verb we track the meaning one phrase at a time:
- Which many disagree?
Many in the government disagree.
- How do they disagree?
Many in the government disagree with a plan.
- Which plan do they disagree with?
Many in the government disagree with a plan to debunk the effort.
- This is where the sentence seems to doubles back on itself semantically. Because they disagree with a plan to debunk the effort, it seems they tacitly endorse that effort.
Many in the government [endorse] the effort.
- Which effort do they endorse?
Many in the government [endorse] the effort to expose the frivolity of Project X.
So on its face, the sentence does suggest that many in the government endorse exposing the frivolity of Project X. For completeness, we include the final modifying phrase, which seems to be less relevant.
- What kind of effort to expose the frivolity?
Many in the government disagree with a plan to debunk the low-budget, grassroots effort to expose the frivolity of Project X.
The sentence is poorly crafted, and the because the conclusion is counterintuitive to our experience of frivolity in government, we naturally do a double-take and ask ourselves. When was the last time many in the government really endorsed exposing a frivolous project?