Is it possible to estimate the cost of acquiring 1 million users for an app similar to tweetdeck, but with different, unique features?
Thank you in advance.
This question is missing lots of details related to your market without which it's difficult to answer reasonably. Before coming to an estimate of amount of expenditure on marketing, you need to think about the way(s) of marketing that you're going use.
Otherwise, you can spend a million bucks and still go nowhere and on the other extreme, can acquire those many users (1m) without spending a significant amount on marketing.
Take a look on this canon question: