Short answer. Silence becomes admission. Each matter in the request shall be deemed admitted unless, within the period designated — never less than fifteen calendar days from service — you file and serve a sworn statement specifically denying the matters or explaining in detail why you can truthfully neither admit nor deny them.
What the law says
Each of the matters of which an admission is requested shall be deemed admitted unless, within a period designated in the request, which shall not be less than fifteen calendar days after service thereof, or within such further time as the court may allow on motion, the party to whom the request is directed files and serves upon the party requesting the admission a sworn statement
Rule 26, Section 2 — Implied admission. Read the full provision →
The trap built into the tool
A request for admission looks harmless — a list of statements the other side asks you to admit or deny. The danger is in what happens if you do nothing: each matter shall be deemed admitted. Not "may be", not "after a hearing" — deemed admitted by the mere lapse of the period. Facts you would have hotly contested at trial can enter the case as established simply because a deadline passed unanswered. The device exists to strip a case down to what is genuinely disputed, and it does that by making silence expensive.
What a proper response looks like
Only one thing stops the implied admission: a sworn statement either denying specifically the matters of which an admission is requested or setting forth in detail the reasons why he or she cannot truthfully either admit or deny those matters. Each element is load-bearing. The statement must be sworn — an unsworn reply is no reply. Denials must be specific — a blanket "I deny everything" does not engage the individual matters. And if you genuinely cannot admit or deny — the fact is outside your knowledge — you must say why, in detail. The response must also be both filed with the court and served on the requesting party within the period.
The clock, and how to stretch or contest it
The request itself designates the period, but the rule sets a floor: it shall not be less than fifteen calendar days after service. If the time is genuinely too short for the matters involved, the court may grant such further time as the court may allow on motion — but you must ask before the period runs out, not after the admissions have already been implied. If the request is itself improper, the rule provides a separate track: objections shall be submitted to the court by the party requested within the period for and prior to the filing of his or her sworn statement, and compliance is deferred until the objections are resolved. Objecting, in other words, is done inside the deadline, not instead of it.
If the period has already lapsed
Do not assume the case is lost, but treat the situation as urgent. Bring the request, proof of when it was served, and the case record to your lawyer immediately: what can still be done depends on how the implied admissions have been used and on the court's disposition, and any relief will have to be asked for, promptly and with a credible explanation. Going forward, adopt the habit the rule punishes you for lacking — calendar every discovery deadline from the date of service, and never let a request for admission sit in a drawer because it "isn't the trial yet." Under this rule, it very much is.