Most of the high-skilled potential immigrants work in the private sector, and the private sector is supportive of the immigrants. Striking work will impact that same private sector more than the government.
So I think its not a good idea to strike work enmasse.
How about some constructive way of spreading awareness?
One idea I have is: Instead of striking work for a day, pick a day and donate the earnings of that one designated day to charity via Rajiv Khanna or IV.
Rajiv Khanna (if he volunteers) or some central responsible entity will collect the number of signatures and one day's earnings from everyone and give it to a charity organization. Make a big banner check and present to charity in front of USCIS/DOS office or in Washington DC. Invite lot of press to cover the event.