Publically funded science DOES affect lives...
The nature of scientific research (which is really quite a simple process, though any particular subject may be horrendously complex) is such that there are several levels of research.
(DAR) Direct applications research: Searching for a solution to an existing problem.
(IR) Investigative research: Looking for the cause & effect relationship in a particular condition (which often assumes some such relationship exists, which is not always the case, and when it does, there may be many different causes.)
(PR) Pure research: Basically mucking around examining the world to see if you can figure out how it works.
(MR) Mathematical research: Playing games with numbers and looking for correlations in the real world. (Games in this sense do not mean 'toys' or 'trivial
(TR) Theoretical research: Research into how to test theories of why and how things work as they do.
ALL of these directly affect your life, though not on the same time scale.
Mathematical research (MR) often takes very long times between a mathematical curiosity and something practical--typically decades to centuries. This sort of research is seldom financed by for-profit concerns, since payback is delayed long past the point of easy profit. Traditionally, this is done by learning institutions, people with intense interest in the subject supported by patrons or society because it eventually proves valuable to society. It seldom pays either researcher or patron a return.
Theoretical research (TR) also often has a long delay between the research and any direct payoff...often the initial stage (in things like high-energy physics, cosmology, astronomy) results in the design of hugely expensive equipment to test the results. This sort of research finds capabilities that we never thought of before the research was done. Again, done primarily by 'Good Samaritans' and those with intense interest and society as a whole. Often no direct financial return, often substantially delayed returns.
Pure research (PR) is exploration. You don't know what you might find, you're not looking for anything in particular except information. It is the basis for much theoretical work, and often finds that we don't understand something as well as we thought we did. Very often, we discover something we already knew, and the exercise generates lots of information in the form of 'thought so.' There is often no direct or immediate payback for (PR.) But occasionally it pays big. seldom financed by for-profit entities.
Direct applications research (DAR) aimed at solving a articular and usually immediate problem, this is about the only form of research routinely financed by for-profit enterprises, often there is an expectation of a very large payback for the expense, and lack of results will often terminate the program. This is commonly financed by military and commercial ventures as well as society as a whole. Much of this financed by public funding finds immediate for-profit use, often with insignificant costs to the for-profit venture, since it was 'publicly funded.' For commercial ventures like drug research, aircraft design and a slew of others, public funding of this research generates immediate profits for industry since they are seldom required to pay the actual costs of the research.
Then there's 'innovation' which, despite popular usage, is not the same as 'invention.' Innovation is basically design tweaking, adding or removing features, making slight changes to improve a particular product. This is incredibly popular commercially because it has low costs, immediate payback and utilizes an exiting market (a new invention needs to have the market educated as to why they would want or need the invention...something seldom readily apparent to people who are already managing without it.)
Of course, these categories are not distinct, and there may be others I've not considered, and most research has elements of all of these.
Innovation won't take your from walking to rockets. Invention will.
Pure research provides the information needed to do applied research...without it, overall advancement slows and stops...though that always takes time.
Mathematical, pure, and theoretical research are the laying of foundations, necessary, but insufficient to directly affect you. E=MC^2 is pure math, and as such, has no direct effect upon your life...the applied results have massive effects on you and society.
Applied research, a better battery, a safer vehicle better understanding of why people do what they do...all are capable of providing immediate and directly observable results (lighter less flammable less explosive batteries, fewer traffic deaths, faster learning, fewer interpersonal conflicts.) Few people have trouble seeing the practical reasons for such research, but its success rests upon the less visible foundations.
The long delays involved make this similar to delaying maintenance on your house or car--you can avoid repainting the house for a couple years at little expense, but eventually, you will find that the repair cost rapidly increases. You can skip an oil change, or prolong it by a thousand or so miles and no noticable problems are likely, but failing to do it at all, will destroy the engine sometime don the road.
Science is a way of investigating the world. As such, it has as it's direct purpose, understanding, rather than creation of functional objects and procedures. Such creation is called engineering, and results in actual deliverable devices and processes on which cost-benefit analysis can usually be easily performed.
Science is like learning to read or write or do mathematics...the advantages are not directly obvious, the advantages come in the secondary effects, the ease with which reading and writing permits you to record and transfer information, to do new things, the ability to calculate your finances so you know not only if you are running our of funds, but why.
Babies are useless on the surface, they do nothing except consume resources--the ultimate example of Mr. Romney's 47% 'non-contributors' but without them, civilization and our species fails.
We publicly fund science because since we developed the technique, it has time and again proven it's overall worth to humanity as a whole, and to a significant number of individuals. We have managed to do more with less resources each year since the scientific age began than in most centuries before that time.
If you were not born into wealth in a perfect body, you owe much of the quality and longevity of your life to the scientific method, even if you were, your life would be significantly less comfortable, entertaining, shorter and more boring without it.
No even truly wealthy king or emperor pre-science had a life that compares favorably with that of a middle-class American.
Science is a process, a way of doing things. That's all. But it is extremely powerful compared with previous ways of doing things. Where it fails, it is not usually the process which has failed, but those using it--people being as they are, they frequently intentionally or otherwise fail to follow the process, usually because the process is not giving them the personally desirable result, usually financially or socially. This is because science done right requires you to be able to take what you thought you knew and discard it in favor of new information, and socially and/or financially scientists often have a vested interest in their current beliefs. Just as day traders have a vested belief in whichever way they are betting the market will move, and nearly everyone has a vested emotional interest in their belief that they are making good decisions.
Belief is valuable and useful, but the facts will, eventually slam into you and hurt if your belief is not in line with them.