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* Bush says he will consider White House bid at 'proper time'
* Rejects suggestions he has backtracked on immigration
By John Whitesides
WASHINGTON, March 10 (Reuters) - Former Florida Governor Jeb Bush appeared on five morning talk shows on Sunday to plug his new book on immigration, but said his heightened visibility does not mean he is re-entering politics or planning a White House run - not yet, anyway.
The talk-show marathon capped a busy week of public appearances for Bush, one of several Republicans seen as potential contenders for the 2016 presidential nomination. Bush said it is too early to seriously ponder a bid for the White House.
"I've decided to defer any consideration of it until the proper time ... which is out more than a year from now, for sure," Bush said on CNN's "State of the Union" show. "When I go through that process, I'll let you know."
Bush's book tour has sparked a torrent of speculation about his political future, but he has shrugged off questions about his plans without definitively ruling out a presidential bid.
"I'm not viewing this as a political re-entry," he told ABC's "This Week" of the media tour for his book. On NBC's "Meet the Press," he described the media as "crack addicts" obsessed with speculation about the campaign.
Bush is one of a handful of potential Republican contenders in the public eye in recent months, a list that also includes Republican Senator Marco Rubio of Florida, Louisiana Governor Bobby Jindal and New Jersey Governor Chris Christie.
Bush has come under fire for appearing to backtrack on his support for a path to citizenship for illegal immigrants. A passage in his book proposes a path to legal residency for undocumented immigrants but tough conditions for citizenship.
"I haven't changed," he said on CBS's "Face the Nation" show. "I support a path to legalization or citizenship so long as the path for people that have been waiting patiently is easier and costs less - the legal entrance to our country - than illegal entrance."
Republicans have become more favorable to the idea of a path to citizenship since losing the Hispanic vote by a big margin in November, and Bush said he backs bipartisan Senate efforts to develop a comprehensive immigration plan led by a group including Rubio.
"This is a very encouraging time, because if we can get immigration right, imagine, there's possibilities of cats and dogs living with one another in other policy areas as well," Bush said.
While Bush's father and brother were both presidents, he said he did not believe he would carry any "Bush baggage" into a possible presidential bid. He said his brother George's unpopular 2001-2009 tenure in the White House will eventually be viewed more favorably.
"I love my brother. I'm proud of his accomplishments. I love my dad, I'm proud to be a Bush and if I run for president it is not because of something in my DNA that compels me to do it," he said on "Fox News Sunday." (Editing by Eric Walsh)