News and information spread over social media can have big impact on thoughts, beliefs, and opinions. It is therefore important to understand the sharing dynamics on these forums. However, most studies trying to capture these dynamics rely only on Twitters open APIs to measure how frequently articles are shared/retweeted, and therefore do not capture how many users actually read the articles linked in these tweets. To address this problem, in this paper, we first develop a novel measurement methodology, which combines the Twitter steaming API, the Bitly API, and careful sample rate selection to simultaneously collect and analyze the timeline of both the number of retweets and clicks generated by news article links. Second, we present a temporal analysis of the news cycle based on five-day-long traces (containing both clicks and retweet over time) for the news article links discovered during a seven-day period. Among other things, our analysis highlights differences in the relative timelines observed for clicks and retweets (e.g., retweet data often lags and underestimates the bias towards reading popular links/articles), and helps answer important questions regarding differences in how age-based biases and churn affect how frequently news articles shared on Twitter are accessed over time.