The federal timeline is 60 days, but it allows for states to set their own timelines:
http://idea.ed.gov/explore/view/p/,root,dynamic,TopicalBrief,4,
The parent also needs to submit a request for evaluation in writing, in order for the clock to start, and even then, the clock doesn't -really- start until the district receives signed consent to evaluate. So it looks like this (I'm using sample timelines from a composite of states which have chosen their own timelines):
1. parent submits written request for evaluation: district has 10 days to respond in writing, with
a. a form requesting consent to evaluate, or
b. with a written notice of why they refuse to act.
2. if a consent form is issued, parent has 30 days to respond to consent:
a. accept in full
b. accept in part
c. accept in full or in part, with requests for additional areas to be evaluated.
d. reject
e. no response (which districts can choose to take as tacit rejection)
3. once consent is signed, the 60 day timeline clock begins. States have various ways of delineating this, such as
a. 45 school or calendar days (states will specify which) to complete evaluation, plus 15 days in which to hold the meeting.
b. 45 days to complete evaluation, plus 15 days from the date evaluation is completed in which to hold the meeting.
c. 60 days to complete evaluation and hold a meeting to review evaluation results, followed by another timeline (often 30 days) to hold an eligibility meeting
d. 60 days to complete evaluation and hold a evaluation review meeting, followed by a timeline to hold an eligibility meeting, followed by yet another timeline to develop an IEP for an eligible child.
So the process can be as short as 2 months, or as long as four or five months. It depends very much on the state in which the student resides. On a side note, though, as soon as the referral process is initiated, the school must extend the discrimination protections owed to a person with disabilities to the student, because they have now been formally notified that this is a person suspected of having a disability. Relevant in such cases as: expulsion of a student who may have an emotional disability, or social pragmatics disability, who may have engaged in disciplinary infractions as a manifestation of his/her disability. "Counseling out" a low-performing or difficult-to-teach student while the evaluation is in process.
For the timeline specific to your state, try the state DOE website, under special education initial evaluation (or eligibility determination) process.