“There’s always free cheese in a mousetrap” means a combination of “there is no such thing as a free lunch,” “you can’t get something for nothing” and “there’s always a catch”—the catch being that the mouse gets caught in the trap. Libertarians have used the saying to mean that “free” government assistance comes at the cost of one’s liberty.
 
The saying probably comes from H. C. Diefenbach, who was quoted in 1950:
   
“I reckon some of us folks who work for a living would be less suspicious of that free government welfare if the do-gooders and political planners didn’t try to make it all seem so easy…Fifty years of struggling to make ends meet have taught me one thing for sure—that you don’t get something for nothing. A mouse will always find free cheese in a mousetrap; but I never saw one that was very happy about it.”
 
“Mice die in mouse traps because they don’t understand why the cheese is free. The same thing happens with socialism” and “Socialism is like a mouse trap. It works because the mouse doesn’t understand why the cheese is free” are related sayings.
 
     
Wikipedia: Anti-proverb
Conservation: The meaning is similar, with and without the supplement: There is no such thing as a free lunch, but there is always free cheese in a mousetrap
 
Google Books
Everyman’s Almanac
Michigan Railroads Association
1936-1955 (The Google Books date cannot be verified—ed.)
Pg. 118:
A mouse will always find free cheese in a mousetrap, but I never saw one that was very happy about it.
 
3 December 1950, Trenton (NJ) Sunday Times-Advertiser, “Quotable Quotes,” pt. 1, pg. 10, col. 6:
“I reckon some of us folks who work for a living would be less suspicious of that free government welfare if the do-gooders and political planners didn’t try to make it all seem so easy…Fifty years of struggling to make ends meet have taught me one thing for sure—that you don’t get something for nothing. A mouse will always find free cheese in a mousetrap; but I never saw one that was very happy about it.”—H. C. Diefenbach.
 
17 February 1951, Racine (WI) Journal-Times, pg. 10, col. 3 classified ad:
A MOUSE ALWAYS FINDS FREE CHEESE IN A MOUSETRAP BUT HE ALSO FINDS IT WAS NO BARGAIN.
(Racine Ford Company—ed.)
 
Google News Archive
13 August 1951, Nevada (MO) Daily Mail, pg. 6, col. 1 ad:
A mouse finds free cheese in a mousetrap…for which he pays dearly!
These Fine Cars Are
No Cheese—No Trap
(Bray-Rogers car dealership—ed.)
 
Google News Archive
24 December 1953, The Cayuga Chief (Weedsport, NY), pg. 1, col. 4:
THE OLD TIMER SAYS:
“There’s always free cheese in a mousetrap, but I never saw a happy a mouse there!”
 
Google News Archive
14 August 1962, The Newberry Observer and Herald & News (Newberry, SC), pg. 4, col. 2:
Other Editors Say…
There is always always free cheese in a mousetrap—but you have never seen happy mouse there.—CHICAGO, (ILL.) AMA NEWS.
 
Google News Archive
15 March 1985, The Daily Record (Ellensburg, WA), “Sale of Canada” by L. M. Boyd, pg. 6, col. :
A wall plaque once offered to legislators debating a welfare bill read: “There’s always free cheese in a mousetrap.”
 
Google Books
The Dictionary of Modern Proverbs
Compiled by Charles C. Doyle, Wolfgang Mieder, and Fred Shapiro
New Haven, CT: Yale University Press
2012
Pg. 37:
There’s always free cheese in a mousetrap.
1962 Dispatch [Lexington NC] 2 Jun.: “Mousetraps furnish free cheese. But the mouse’s happiness there is short-lived. For mice and men there is no such thing as a free lunch.”
1962 Nevada [MO] Daily Mail 1 Oct.: “Looking for a government handout? There’s always free cheese in a mousetrap, but you never saw a happy mouse there.”