"Chavez nationalized oil companies, censored opposition media and banned guns. Democrats lost a true believer," Stockman posted to his Twitter account.
The post was deleted three seconds later, but archived by Politwoops, a website that chronicles deleted tweets from politicians.
Stockman's tweet was not the only controversial lawmaker reaction posted to social media. The Republican National Committee seized on a tweet praising Chavez posted by Rep. Jose Serrano (D-N.Y.) shortly after the Venezuelan leader's death.
"Hugo Chavez was a leader that understood the needs of the poor," Serrano wrote. "He was committed to empowering the powerless. R.I.P. Mr. President."
A spokeswoman for the RNC called that tweet "simply insulting."
"Chavez systematically cracked down on the basic freedom and liberties of Venezuelans, nationalized private industries, and befriended anti-American dictators like Castro, Ahmadinejad and Assad. Americans should stand together with the freedom loving people of Venezuela as they hope for a peaceful transition to a democracy, instead of praising the former dictator," the RNC statement read.