OpenSSL des-ede3 not producing same output as test vector implies it should be
It looks like there's an error in the test vector.

The text of Appendix B.1 states:


  P1 = “The quic” = 5468652071756663


... which is incorrect.

The hex encoding of The quic is actually 5468652071756963 (note the transposition of the i/69 to an f/66 in the encoding.

e.g. encrypting the test vector as intended:

$ echo -n 'The quick brown fox jump' | openssl  des-ede3 -nosalt -nopad -K '0123456789ABCDEF23456789ABCDEF01456789ABCDEF0123'  | xxd -c 8 -ps
1ccf23869d09333e
cce21c8112256fe6
68d5c05dd9b6b900


... and encrypting the test vector as hex encoded:

$ echo -n 'The qufck brown fox jump' | openssl  des-ede3 -nosalt -nopad -K '0123456789ABCDEF23456789ABCDEF01456789ABCDEF0123'  | xxd -c 8 -ps
a826fd8ce53b855f
cce21c8112256fe6
68d5c05dd9b6b900


It looks like this error has been in NIST SP 800-67 since version 1 in 2004.