A zoo or a circus often feeds red meat to its large animals, such as lions and tigers. In politics, a “red meat” issue is one that a particular constituency strongly supports. A politician desires to throw “red meat” to win over independents and undecided voters, but a politician also needs to “throw red meat at the base” to keep those voters satisified.
 
“Red meat” has been cited in a political context since at least 1950 and 1952. Spiro Agnew, vice president of the United States from 1969-1973, often said that he gave “red meat” to reporters to attract their attention. In the 1980s, Ronald Reagan and George H. W. Bush were said to have thrown red meat at their base of political support (the conservative right).
 
     
(Oxford English Dictionary)
red meat, n. and adj.
fig. A source of (spiritual) nourishment; a thing which inspires great enthusiasm or desire.
1933 E. O’Neill Ah, Wilderness! i. 24   Poetry’s his red meat nowadays, I think—love poetry—and socialism, too, I suspect.
1992 Harper’s Mag. Mar. 35/1   It’s pointless‥to study the good or try to keep up with the real when the novelist’s red meat is now, was then, and ever will be his imagination.
2007 Independent 6 Mar. 25/3   The idea is you set up a straw man or woman and attack them‥. This is classic red meat for the partisans.
 
Chiefly U.S. Of an issue, topic, etc.: key, fundamental; likely to rouse strong feelings.
1968 Abilene (Texas) Reporter-News 10 Oct. 10 b/3   The thumbnail description of what each presidential candidate has to offer is about the only red meat issue in this campaign.
1980 N.Y. Times 6 Nov. a25/5   They were referring to the blend of cultural conservatism and political conservatism that went into what were described as Mr. Reagan’s ‘red meat’ speeches.
 
11 November 1950, Oregonian (Portland, OR), “Feuding Bad for Truman Now” by Doris Fleeson, pg. 6, col. 4:
WASHINGTON, Nov. 10—From the power standpoint, the American people have put President Truman on an austerity diet and handed all the rich, red meat to the Taft wing of the Republican party.
 
9 July 1952, Rockford (IL) Register-Republic, “Taft Supporters Seek Party Harmony,” pg. 2A, col. 4:
Earlier he (Dwight D. Eisenhower—ed.) told the Oklahoma delegation that if elected president he will insist that all federal office holders appointed by the Democrats be “cleaned out and replaced by a fresh group”—a campaign pledge that was red meat to the long-starved GOP politicos.
   
12 July 1970, Trenton (NJ) Evening Times, pt. 3, pg. 3, col. 2:
The New Agnew Still Likes
“Red Meat,” But Not Too Raw
By DON BACON
Newhouse News Service
(...)
Lest anyone think he’s growing soft, the vice president (Spiro Agnew—ed.) says he will continue to be outspoken—to throw, as he puts it, “A little red meat” to the masses.
 
19 July 1971, New Orleans (LA) Times-Picayune, “Agnew Attracts Attention Again During World Trip” by Carl P. Leubsdorf, sec. 3, pg. 8, col. 6:
MADRID, Spain (AP)—Vice President Spiro T. Agnew, for the third time on his current world trip, has demonstrated that one of the best ways for him to get public attention is by deliberately throwing some “red meat” to the press.
 
21 October 1981, Seattle (WA) Daily Times, “Former Interior Secretary Andrus says Watt should be replaced” by Eric Pryne, pg. C1, col. 3:
“He’s doing exactly what Ronald Reagan wants,” Andrus said of Watt. “Right now, he’s an asset to the Republicans’ fund-raising, because he’s on the road making speeches, throwing some red meat to the animals.”
   
13 March 1983, Boston (MA) Globe, “The Administration,” by William Beecher, Focus section, pg. 1: 
“He feels the need every three or four months to throw some red meat to the right wing,” the State Department official declared.
 
30 April 1983, Baltimore (MD) Sun, “Reagan takes first jab of ‘84 at Mondale” by Robert Timberg, pg. A1:
At gatherings of the party faithful, such as the Tower fund-raiser, “one of the things you do is throw out red meat to the right people,” he said.
 
Google Books
Backfire:
A history of how American culture led us into Vietnam and made us fight the way we did
By Loren Baritz
New York, NY: W. Morrow
1985
Pg. 119:
It was already obvious that the young President (John F. Kennedy—ed.) believed he had to throw red meat to the right wing rather than risk acting wisely.
   
Google Books
The American Elections of 1984
By Austin Ranney; American Enterprise Institute for Public Policy Research.
Durham, NC: Duke University Press
1986
Pg. 132:
He (Ronald Reagan—ed.) also habitually throws some red meat to the true believers and then promptly ignores the ...
 
Google News Archive
15 September 1988, Toledo (OH) Blade, “Case for the ‘Nobody’s Perfect’ button” by William Safire, pg. 8, col. 3:
The more the Bush campaign throws red meat to the yahoos, the less I like my fellow Republican.
 
Google News Archive
16 September 1988, Reading (PA) Eagle, “Bush waffling on abortion-ban platform” by Ellen Goodman, pg. 6, col. 3:
He (George Bush—ed.) went from feeding red meat to the right, to proffering a well-balanced meal to the middle.
 
Google Books
Dead Certain:
The presidency of George W. Bush
By Robert Draper
New York, NY: Simon & Schuster
2007
Pg. 374:
Even as he (George W. Bush—ed.) flung red meat to the base during the South Carolina primary, he never rose to the bait when town hall questioners invited him to criticize illegal aliens.
 
Crush Liberalism
Perry gives some red meat to the base, along with some fava beans and a nice Chianti…slurp-slurp-slurp!
August 19, 2011 - Posted by crushliberalism
I may have embellished the last part of the post title a tad…but not much.