Best way to store large data set using R from Twitter?
Find a way to make your program write to disk periodically. Keep count of the number of tweets you grab and save after that number is high. I don't write R but psuedocode might look like:

$tweets = get_tweets();
$count = 0;
$tweet_array = array();
for each ($tweets as $tweet) {
  $tweet_array += $tweet;
  $count++;
  if ($count &gt; 10000) {
    append_to_file($tweet_array, 'file_name.txt');
    clear_array($tweet_array);
  }
}