|Ed Platt and Don Adams in "Get Smart"|
Nunes received a secret phone call upon which he bailed out of Uber cab driving him and disappeared into the night. By some mysterious means (picked up by a Russian agent, another Uber driven by a sexy femme fatale, took the Metro) he is transported to the White House whereupon he walks in without a security check because after hours security is lax.
Who Did He Meet?
Nunes saw his secret contact, let's call him Shallow Throat, at the White House. Unless Shallow Throat was a White House staffer he had to be checked in by security, making the meeting far from clandestine.
Nunes pledges to keep Shallow Throat's identity secret. His colleagues on the Intelligence Committee all have top secret clearance so it's not a national security issue. Perhaps it was embarrassing, he could have been meeting a hooker with upstairs access.
Much more likely is that Nunes is involved in a criminal conspiracy and reveling his contact would be self-incriminating.