Can a 20 amp circuit have a 14 gauge pigtail directly to one receptacle?
National Electrical Code 2008
Article 210 Branch Circuits
II. Branch-Circuit Ratings
210.19 Conductors — Minimum Ampacity and Size.
(A) Branch Circuits Not More Than 600 Volts.
(2) Multioutlet Branch Circuits. Conductors of branch circuits supplying more than one receptacle for cord-and-plug connected portable loads shall have an ampacity of not less than the rating of the branch circuit.

Which means in your case, you'll have to use 12 AWG conductors for attaching the receptacle.
note: A duplex receptacle actually counts as two receptacles according to NEC
However, there are situation were 14 AWG conductors can be used on a 20 ampere circuit.

(4) Other Loads. Branch-circuit conductors that supply loads other than those specified in 210.2 and other than cooking appliances as covered in 210.19(A)(3) shall have an ampacity sufficient for the loads served and shall not be smaller than 14 AWG.
Exception No. 1: Tap conductors shall have an ampacity sufficient for the load served. In addition, they shall have an ampacity of not less than 15 for circuits rated less than 40 amperes and not less than 20 for circuits rated at 40 or 50 amperes and only where these tap conductors supply any of the following loads:
(a) Individual lampholders or luminaires with taps extending not longer than 450 mm (18 in.) beyond any portion of the lampholder or luminaire.
(b) A luminaire having tap conductors as provided in 410.117.
(c) Individual outlets, other than receptacle outlets, with taps not over 450 mm (18 in.) long.
(d) Infrared lamp industrial heating appliances.
(e) Nonheating leads of deicing and snow-melting cables and mats.

Check the Device

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Push in #14 CU solid wire for 15A branch circuit only.
Installation Screw Terminal &gt; #14 - #12 AWG CU Wire Only.

Notice on the back of this 125V 15A duplex receptacle, it states that you can use 14 AWG or 12 AWG copper wire when terminating at the screw terminals, but that 14 AWG copper must be used when terminating at the push in terminals. It also says that if you're using the push in terminal, and 14 AWG copper, it can only be used on a 15 ampere circuit. If you're installing this on a 20 ampere circuit, with 12 AWG wire, you'll have to use the screw terminals.