No, but statutes of limitations generally allow at least one year. Except for when you sue a government agency, you almost always have at least one year from the date of harm to file a lawsuit, no matter what type of claim you have or which state you live in. In short, you should have no statute of limitations worries if you sue within this one-year period.
Example: Henry is injured in an auto accident on February 1. On March 1 of the same year, a lawyer whom Henry hires recommends that he seek compensation for his injuries from the driver of the other car. Henry spends months trying to settle with the other driver's insurance company. Finally, on September 1 of the same year, the insurance company writes to Henry that "We'll pay you $1,000, nothing more." Henry concludes that the offer is grossly inadequate and decides to sue the other driver. If Henry isn't sure of his state's statute of limitations for personal injury cases, he should be sure to file the suit by February 1 of the next year and his complaint will definitely be timely.
For various statutes of limitations in your state, see Chart: Statutes of Limitations in All 50 States.
Once you file a complaint on time, a statute of limitations has nothing to do with how long it takes for a case to conclude. However, most states do have separate "diligent prosecution" statutes, which require you to move your case to trial within a certain time period or face dismissal.