No, it is not possible to bind a key to an input.
The closest thing that I found you can do is abuse ngRepeat's $index property and bind it to the input.  You can't change keys for existing values but you can change what value is shown as well as create new key-value pairs.  By no means am I recommending this as a solution, I just wanted to share the hackery that ensued when I was investigating this question.
JSFiddle: http://jsfiddle.net/DanielBank/v6tFG/
JavaScript:
function ctrl($scope){
    $scope.obj = {
        '0': 'a',
        '1': 'b',
        '2': 'c',
        'George': 'Clooney',
    };
}
HTML:
<div ng-app>
<div ng-controller="ctrl">
    <div ng-repeat="value in obj">
        <input type="text" ng-model="$index"/>
        <input type="text" ng-model="obj[$index]"/>
        <input type="text" ng-model="value"/>
    </div>    
    {{obj}}
</div>
</div>