Why are move semantics for a class containing a std::stringstream causing compiler errors?

How can I make this simple class movable? What I thought was correct just produces a wall of errors...

#include <iostream>
#include <sstream>
#include <utility>

class message
{
    public:
        message() = default;

        // Move constructor
        message( message &&other ) :
            stream_( std::move( other.stream_ ) ) // Nope
        {}

        // Move assignment
        message &operator=( message &&other )
        {
            if ( this != &other )
            {
                stream_ = std::move( other.stream_ ); // Nope #2
            }
            return *this;
        }

    private:
        message( const message & ) = delete;
        message &operator=( const message & ) = delete;

        std::stringstream stream_;
        // Other member variables omitted
};

int main()
{
    message m;

    return 0;
}

Compile:

$ g++ --version
g++ (Ubuntu/Linaro 4.6.3-1ubuntu5) 4.6.3
$ g++ -Wall -Wextra -std=c++0x move.cpp -o move

... and get a wall of errors about the copy assignments being called for various base classes of the stringstream.

move.cpp: In constructor ‘message::message(message&&)’:
move.cpp:12:40: error: use of deleted function ‘std::basic_stringstream<char>::basic_stringstream(const std::basic_stringstream<char>&)’
In file included from move.cpp:2:0:
/usr/include/c++/4.6/sstream:483:11: error: ‘std::basic_stringstream<char>::basic_stringstream(const std::basic_stringstream<char>&)’ is implicitly deleted because the default definition would be ill-formed:
/usr/include/c++/4.6/sstream:483:11: error: use of deleted function ‘std::basic_iostream<char>::basic_iostream(const std::basic_iostream<char>&)’
In file included from /usr/include/c++/4.6/iostream:41:0,
                 from move.cpp:1:
/usr/include/c++/4.6/istream:774:11: error: ‘std::basic_iostream<char>::basic_iostream(const std::basic_iostream<char>&)’ is implicitly deleted because the default definition would be ill-formed:
/usr/include/c++/4.6/istream:774:11: error: use of deleted function ‘std::basic_istream<char>::basic_istream(const std::basic_istream<char>&)’
/usr/include/c++/4.6/istream:57:11: error: ‘std::basic_istream<char>::basic_istream(const std::basic_istream<char>&)’ is implicitly deleted because the default definition would be ill-formed:
/usr/include/c++/4.6/istream:57:11: error: use of deleted function ‘std::basic_ios<char>::basic_ios(const std::basic_ios<char>&)’
[SNIP]

... This goes on for several pages.

What's wrong with my code?

Update 1: Clang 3.0 fails with similar results.
Update 2: g++ 4.7 fails also.
Update 3: Using the answers as a guide, I found this: c++11 status in libstdc++ - "27.5 Iostreams base classes: Missing move and swap operations on basic_ios." Curses!