goodroi - 11:31 am on Jan 17, 2013 (gmt 0)
I think you are touching on two different issues.
Issue #1 - Safe Growth Rate of Backlinks
If you have a dramatic boost of backlinks in a short term, your site may trigger a tripwire. What you describe does not sound like a dramatic growth in my humble opinion. 60 domains in 60 days averages out to 1 new linking domain each day and that is not very dramatic.
Issue #2 - Google's Algorithm Timeline
Google's algorithm definitely needs a bit of time to fully digest and properly rank a website, especially a new website. The algorithm has become very complicated with multiple sub-parts. Some parts of the algorithm are run daily, other pieces run every few days and some other parts need to be manually run which can take a very long time to occur.
Without seeing your site I can't say what is happening but I would suggest you look at the types of links that have been added. Are the 60 domains linking to you using massive run-of-site links with identical anchor text?