Would civil disobedience work?

[blaurentnv]

I had a thought that I'd like to toss out there and see what happens with it. In the past, civil disobedience has been an effective tool to overturn unjust laws. What would happen if every same sex couple who is not married, but would be willing to be married, went to the county clerk's office as often as possible. Each time, said couple should politely request a marriage license and politely insist on hearing that it is not available from the actual county clerk. Smother them with kindness; be polite but time consuming. This would make it difficult and time consuming for anyone who wants a marriage license to be able to get them.

Similar techniques in the 60's brought visibility to racial injustice.