Your employer almost always has the right to turn down individual days off. What they do not have is the right to is to always refuse your time-off requests so that you do not get to use it before it expires.
the CA Government says this on their website about time off (dir.ca.gov/dlse/faq_vacation.htm ):
Q. Can my employer tell me when to take my vacation? A. Yes, your
employer has the right to manage its vacation pay responsibilities,
and one of the ways it can do this is by controlling when vacation can
be taken and the amount of vacation that may be taken at any
Since this is written by the department that administers the law and you can see that they clearly state your employer has the right to manage when time off is taken, it seems that a legal suit would be unlikely to go your way.
The reason for this is the employer has to manage workload. If I run a restaurant, I can't have all employees take off the same day or the business can't operate. So as a manager, I have the absolute right to determine if a day off is possible on that particular day. This is why, for instance, you generally have to schedule large periods of leave so that too many people are not requesting the same Chrstmas week time off. When you are on vacation, the work still has to be done.
Smaller companies often have more flexibilty in how much they can say no as well as one employee being out impacts a company of ten more than a company of 10,000.
I know I had at least one job where we could not take more than one day in a row without scheduling a full month in advance or bringing in a docotor's note. Check your company HR policy manual to see what rules they have.
Most managers try to approve most leave, unhappy employees are employees who leave after all. But sometimes it is not possible or it appears the person is abusing the leave by always taking off when there is a time crunch or taking 5 days off in a two week period with no advance notice or calling in sick after a day off was disapproved can all result in dispapproval of your requests.
And sometimes the manager has to balance the needs of others, so that too many are not gone at once. If I have to take every Friday morning off to go get dialysis, that is likely to trump your desire for a long week end if one of us has to be there. And if you got the Thanksgiving week off, then someone you work with would have priority for the Christmas week in most places becasue no one has the right to always get the most desired days off at everyone else's expense.
If your manager has disapproved your leave, then you should not take it unless you want to hire a lawyer to fight for the right take it, if a lawyer is even willing to take such a case. In any case, there are likely to be negative repercussions at work. If the boss has said no you can't take Tuesday off, he is unlikely to be happy with you if you do anyway. That is just career suicide.