Many of us who ride for transportation would dispute that cycling is just recreational. Also a significant number of miles people drive in cars, including me, are also recreational. If I drive back and forth to work all week that is about 100 miles. If I drive to the beach of mountains for the weekend that is 200-400 miles.
I poked around a little and found some things in the documents our country is built on that I would interpret to cover the support of cycling infrastructure. The Declaration of Independence includes the words pursuit of happiness. All the cyclists I know riding for transportation would say that cycling gives them more happiness than driving. The Declaration of Independence goes on to say government should organize its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. So if the government is building transportation infrastructure it seems imperative to consider the safety of all users. After all we don't let the truckers just do what they want. There are plenty of rules to make their use of the transportation network safer. The same is true of trains and planes.
It seems like I could go on and on, but I will stop here and see if others would like to comment.
On a related note, Tom Bowden had an article on Commute By Bike discussing How to Talk About Cycling to a Conservative that is worth a read.