As I understand it, and I don't claim to be an expert, significantly lower launch costs will have a compounding effect on other costs. I am talking about lowering costs by 2 orders of magnitude. That means putting a pound in LOE for $100 instead of $10,000 as is now the case.
The biggest current cost of R&D is making the systems as fool proof as possible because you only get one shot due to the launch expense. There is a serious diminishing return problem that means costs escalate dramatically to get relatively small increases in reliability.
When launch costs are dramatically reduced it will be possible to carry lots of back up systems and spare parts on your ship, instead of having to make that one system that you have perfect. The extra systems and spare parts will cost less than that R&D.
Equipment will no longer need to be hand crafted for specific missions. Exploration missions will be able to use, to a large extent, off the shelf components being mass produced for the burgeoning commercial space market.
I would expect a $50 billion Mars mission would have it's costs reduced to something like 1 or 2 billion.
Mind you I'm just talking off the top of my head, I don't have detailed analysis to back this up, but I do believe it is a fundamentally reasonable line of thought.
I further think that the average citizen is quite willing to spend money on exploration, it's just a question of how much. Bring down the costs and it will be no problem getting ample support.