I'm growing a pumpkin patch and plan to use drip irrigation under a mulch layer.
Unfortunately, various parts of the soil are lacking in some nutrients. I don't think I'll have the money (this year) to broadcast the needed soil amendments. Ergo, my question is: Can I fertilize solely by fertigation and make an impact on my crops?
Not really, if you want good results, but you probably don't need to worry about whatever nutrients you're aware are lacking in whatever area of soil, though you've not mentioned what they are.
If you enrich the soil first with plenty of humus rich materials, particularly composted manures, dig that in, then plant, it should be fine. These plants are greedy feeders and prefer rich soil, so if you don't emend the soil first, you won't get such good results with simple fertigation. Three or four 60 litre large bags of composted manure isn't that expensive (well, not in the UK anyway, but I can't imagine it'd be hugely expensive where you are either). You should use high nitrogen fertigation when the plants are about a foot tall, just before they start running, then switch to one high in phosphorus just before bloom time. Use an organic mulch rather than chippings or stones.
