This will perhaps be clearer if you recast it a little to sidestep the it ... BE for VERBing idiom. That will give something like this:
If an out-of-state lobbying group ___ (not infuse) cash, the initiative would not have garnered enough signatures to qualify.
Would ... have garnered in the consequence clause is clearly both counterfactual and past-tense, and since we're dealing with an actualization conditional the construction of infuse at "__" in the condition clause must likewise be both counterfactual and past-tense. Use of a past-tense verbform (infused in the positive, but did infuse in the negative) would express non-past counterfactuality:
* If an out-of-state lobbying group did not infuse cash, the initiative would not have garnered enough signatures to qualify.
To shift a past-form verb expressing counterfactuality into past-tense reference, we employ the perfect construction as a past marker:
If an out-of-state lobbying group had not infused . . .
In the same way, If it weren't for... provides only the modality shift; you need If it hadn't been for... to shift both tense and modality.
However, it must also be observed that this degree of grammatical precision is more than most people practise or demand in any but the most formal discourse; If it weren't for... will go unremarked in ordinary speech.