Strictly speaking, she wasn't their kind -- her husband had never served in that exclusive club called The Congress. But yesterday it hardly seemed to matter, as 200 members of The Congressional Club welcomed first lady Nancy Reagan to their New Hampshire Avenue clubhouse.

As it turned out, there were more than handshakes awaiting her. There were also some smoke-filled rooms, which got that way when three fireplaces started belching smoke caught in downdrafts.

"Oh, my gosh," moaned Ruth Frenzel, wife of Rep. Bill Frenzel (R-Minn.), "we'll never see her."

"I feel like a smoked flounder," quipped Lou Engle, widow of Sen. Clair Engle of California.

"They ought to be playing 'Smoke Gets in Your Eyes,' " said Carolyn Long, wife of Sen. Russell Long (D-La.).

"Smells like someone lit a torch to it," said James Rosebush, the first lady's chief of staff.

Unconcerned by it all was Nancy Reagan, who never shivered once in the gush of fresh air streaming through open doors and windows as she and club president Norma Lagomarsino, wife of Rep. Robert J. Lagomarsino (R-Calif.), shook everybody's hand.

Upstairs, Mrs. Reagan circulated, stopping to talk for several minutes with Mary Andrews, wife of Sen. Mark Andrews (R-N.D.), who was making a rare appearance at the club. The North Dakota senator's wife has been confined to a wheelchair since she was stricken with bacterial meningitis in December 1979.

Norma Lagomarsino, whose husband is President and Mrs. Reagan's congressman (the Reagan ranch is in his Santa Barbara district), decided to invite the first lady to the informal coffee at the clubhouse so everyone could have a chance to meet her.

"Rosalynn Carter never came to this building once," said Lagomarsino, "because no one ever asked her."