The 'right' answer on this question is going to depend on your own situation. If you 100% can not put in overtime, extra shifts or weekend work, say so; and if possible explain your situation while not disclosing any information that can be used to discriminate against you.

An example might be that you are taking additional classes and need that time for schoolwork and projects. If you take care of another person then that is also a valid reason.

If you do have other commitments but can work extra hours with a reasonable notice, now would be a good time to establish that notice period. For most companies, providing a week or possibly two should be able to be accommodated.