“Ancient Rome declined because it had a Senate; now what’s going to happen to us with both a Senate and a House?” is attributed to humorist Will Rogers (1879-1935). Rogers actually said in January 1927:
 
“I stood in the Roman Forum, and I found out that they had a Senate in Rome long ago. That’s why Rome declined. Boy! If they declined with a Senate, what will we do with a Senate and a House?”
   
Will Rogers had been hired by the Saturday Evening Post in 1926 to travel to Europe and write exclusive articles. His compilation book, Letters of a Self-Made Diplomat to His President. Vol. 1. (1926), said that Rome did have a House of Representatives:
 
“There is quite a few of those old Forums besides the Senate one. Evidently they were afflicted with a House of Representatives, a Supreme Court and a Foreign Relations Committee. ‘Course it’s just a lot of old broken-down Marble now.”
     
 
Wikiquote: Will Rogers
William Penn Adair Rogers (4 November 1879 – 15 August 1935) was an American humorist and entertainer; known primarily as Will Rogers.
 
Sourced
Ancient Rome declined because it had a Senate; now what’s going to happen to us with both a Senate and a House?
. As quoted in Dreams Come Due: Government and Economics as If Freedom Mattered (1986) by John Galt, p. 235
   
Google Books
Letters of a Self-Made Diplomat to His President. Vol. 1.
By Will Rogers
New York, NY: A. & C. Boni
1926
Pg. 108:
There is quite a few of those old Forums besides the Senate one. Evidently they were afflicted with a House of Representatives, a Supreme Court and a Foreign Relations Committee. ‘Course it’s just a lot of old broken-down Marble now.
 
29 January 1927, New York (NY) Times, pg. 2:
ROGERS SATIRIZES
OUR FOREIGN POLICY
Every Time We Go on a Mission
We Come Back With Both
Legs in a Sling, He Says.
SYMPATHIZES WITH CHINESE
“Why Spoil Their War?” They Get
Few Pleasure Out of Life, He
Tells Audience at Town Hall.
Will Rogers, the philosopher-Mayor of Beveryly Hills, Cal., came to town yesterday with doleful comments on the Administration’s trouble in Nicaragua, Mexico and China, all of which he ascribed to a meddling desire to be “helpful.”
 
“Every time we start out on a humanitarian mission we come back with both legs in a sling,” said Mayor Rogers from a stage of the Town Hall before an audience of 1,500 women at a meeting under the auspices of the League of Political Education.
(...)
Mayor Rogers described his recent trip to Rome and his interview with Mussolini. “I stood in the Roman Forum, and I found out that they had a Senate in Rome long ago,” he said. “That’s why Rome declined. Boy! If they declined with a Senate, what will we do with a Senate and a House?”
   
Google Books
Will Rogers, Ambassador of Good Will, Prince of Wit and Wisdom
By Patrick Joseph O’Brien
Philadelphia, PA: John C. Winston Co.
1935
Pg. 136:
In describing his trip to Rome and his interview with Mussolini, he said: “I stood in the Roman Forum and I found out that they had a Senate in Rome long ago. That’s why Rome declined. Boy! If they declined with a Senate, what will we do with a Senate and a House.”