"The US govt *could* if it wanted to spend less than 1 billion dollars and start rocket fuel market in space. "

Btw, it isn't required that US govt do this- other govts or simply a billionaire could choose to do this.

What is needed most is technology that can make LH&LOX in orbit from water. Making LH&LOX on earth or the Moon is different matter than making LH&LOX in microgravity. So we need the technology and need it shown to work.
So, take a ton of water and turn it into a ton of LH&LOX [Or
222 lbs of LH and 1777 lbs of LOX] in orbit.
There is not one way to do this, nor do we know the cheapest way to do this. And if the technology is developed it won't necessarily be the best way to do it.
To give a basic example of what I mean. Instead using electrolysis, you might use something that could use more energy but has other advantages. For instance you might use aluminum:
http://www.habitablezone.com/space/messages/469621.html
I'm not claiming this is the solution, but it's possible.
As another example of different things one could do- instead using solar panels, you might beam microwave energy from Earth.
What technology is developed could more to do with short term or long term business plan than other factors.
The other factors are there are more than just the splitting of water- there is the storage of LH&LOX and the ability to cool these substances, docking spacecraft, and refueling spacecraft.
But focusing on using water as a source of rocket fuel is important, because there is a lot of water in space. If water isn't minable on the Moon, then there are other known sources of water in the space environment which could be minable. Water is easier to ship and store than compared to LH&LOX [or other rocket fuel].

Now to the main point. Where and what in space would be most minable water. You are God, you want to put water in space, so the Earthlings would consider it worth going to and mining it to make rocket fuel.
Now, to me the Moon seems like a pretty good choice, but where would be even better place- easier to mine. A dead comet in Earth orbit would be easier to mine.
Now, if there was nice size dead comet in Earth orbit with say 90% water, the stupid humans might have war over it, and/or they may tax it or turn it into an Antarctic in space- so it might be a very costly thing this dead comet- it might cause less damage if impacted earth. But leaving aside all the political an legal problems, how much would it cost to mine the water. It wouldn't be easy to determine this, you need to determine how much of market there would be over time- if the sole "market" was that water was going to be used for Manned Mars- it could be quite expensive to mine the water because that could be a small market.

So, ask a different question. If water was in a tank in orbit, what would the least of water that would be needed in that tank for it to be worth going to- in order to take the water turn it into rocket fuel and sell the rocket in order to pay back the costs and make a profit. In other words a 1 ton of water or a fifty thousand oz gold may not be worth the trip.
10 tons of water of 1/2 million oz of gold may be worth the trip- 1/2 million oz of gold would be more valuable than 10 tons of water- because it's easier to get it and sell it.
But a 100 tons of water may be worth more than 1/2 million oz of gold. And 100 tons of water could lead to situation that getting the 50 thousand oz of gold could be worth getting.
Said differently, 100 tons of water in earth orbit in one location, could be worth more than 10 groups of 50,000 oz gold scatter around in various Earth orbits.
Water can be seen to be as valuable as it's usefulness as a propellent, but I think and I will explain that the 100 tons of water is much more valuable to be made into LH&LOX than to merely be used as a propellent [such for a steam rocket or propellent for microwave rocket]. But first, I'm going to explain how you could get 100 tons of water in orbit for free.

Nothing is free. But doing things cheaper, can make money, therefore one can borrow capital, pay back what you borrowed, and make more money than borrowed including the interest rate charged. In a word, Capitism.

So, in this case, what can be made cheaper is rocket payload costs. There many reasons why payload are costly- $2000 more or less per lb to LEO. But the simplest and main reason is lack of market demand. Now a spike in demand, of course increases the price, but more market demand over long periods of time, lowers the price- on anything. Something Socialists can't seem to grasp. This rule assumes humans aren't enslaved and able of employ their modest intelligence. So more market demand would lower the cost and price of rocket payload- assuming something is not interfering [such as govt laws or other monopolies of power]. Walker generally goes over this here:
http://www.fourmilab.ch/documents/rocketaday.html

So, a rocket company can give a better price per lb for 100 tons of payload than for 10 tons of payload. And a rocket company that can deliver the 100 tons of payload in any timeframe can be done cheaper than if it done on a required timeframe. In other words if required to deliver 100 tons within a year or over 10 years [say 10 tons a year] then that is more expensive than delivering 100 tons in whenever within say 5 years.
So, if there was a demand such as will pay for as many payload as you can deliver for next 20 years, that could lower the cost of delivering payload- you could probably lower the cost down to $100 per lb [this assuming you have a competive launch market]. Now if you launching payloads which cost 100 million dollars and the rocket explodes or fails in anyway then that is expensive. But if the payload is the cost of water [nothing] and the price of the tank- hundreds to thousands of dollars, then the main cost is the rocket itself.
So, if the govt offer to buy water payload and will buy 100 tons and will offer to pay $500 per lb of water payload- this costs govt when the payload are delivered a total of 100 million dollars. And what the govt can do with those water payload is turn around and offer to give those 100 tons to any party that will launch something that will convert water into LH&LOX [which they can do whatever to like to do with it- maybe sell it to govt or sell to private sector].
Now, this essentially cost the govt nothing. Because rocket are being tested water payload instead of govt payloads [govt has lost billions dollars due to rocket failure- if this program reduce that failure by 5-10% it making money- on that aspect alone. Second, it will lower payload cost for satellites- and in just aspect could save more money than the 100 million spent.
Now, if 100 tons is good idea, then perhaps some will think more of it would be better. And to a certain extent this is true, BUT the govt would not need to spend very much more money because if it gets gas station built, then the gas station owner could buy these water payloads.

But as I said before different inclination in LEO are worlds apart, so govt might want to buy 100 tons of water in say two different inclinations- and which inclination could decide on by what launch locations put water payloads into orbit. So, that is 200 million in total cost.
Next I said that L-1 was critical, so put 100 tons to L-1- offer to give say $1000 per lb. So, total cost is 400 million.
Now, if govt offers these prices and no one bites for couple years, increase the offer. So say it costs twice the price [seems excessive to me, but] so that a total of 800 million- still around the cost of a Shuttle launch and even if 800 million still probably cost less than compared without such a program. And of course govt could get to use [but not spend any money on operational cost] 3 gas station- which could significantly lower cost of moon mission and make Mars manned dirt cheap.
So along the way I think I've explained how making LH&LOX in orbit is valuable- saves tens of billions of dollars at least.