I have a question about ICs with contracts/new jobs - hoping you guys can help (sm)

Do most ICs who sign contracts requiring 30-day notice adhere to that?  I cannot see myself working two full-time jobs, as I oftentimes have trouble meeting minimum line count requirements at the current job because changes seem to come along about every 90 days or so, just when I am getting used to things and am finally able to consistently make the line count.  I guess I fear that if I tell the new job I cannot start for 30 days (or even two weeks for that matter) they will not hold the position for me, but I do not want to burn any bridges behind me in case I ever need to go back the way I came.  Also, wondering if it is worse than just burning a bridge and if I could find myself in court (do they really take the time/money to take one to court who signed a contract but no longer wishes to work for them).  And, of course, the other thing would be that if the new company would hold the job, the current company would release me before the 30 days is up and would possiblly not have an income in the interim. 

I have not yet tested or gotten another job, but the contract and above questions are part of what is holding me back from going for it.  I know who I want to apply with, and a big reason is that I want to be an employee rather than an IC (for tax purposes).  I would love to hear your thoughts on this and hear about the experiences others have had with this. 

Thanks!