The apalike bibliography style has been around more or less unchanged since 1988. Back then, web pages didn't exist yet -- at least not as items that might be cited in bibliographies. The entry type @misc thus doesn't recognize, and hence blissfully ignores, fields named url, urldate, and lastchecked.
A workaround involves these steps:
- rename the field
Lastchecked to note,
- modify the contents of the
note field from Nov 01, 2013 to Last accessed on Nov 01, 2013, and (optionally)
- encase the URL string in the
howpublished field in a \url{...} wrapper.
Separately, you should also encase the contents of the author and title fields in pairs of curly braces. This prevents BibTeX from (a) misinterpreting the author as a person with first name Editor and last name CNN and (b) lowercasing the words Supreme, Court, and Emanuel in the title field.
Aside: If you need to cite a lot of web pages, you may be better off in the long run choosing a bibliography style which does know what to do with fields named url, urldate, and lastchecked.
Here's an MWE that implements these ideas. Note the changes I applied to the following fields: author, title, howpublished, and urldate (renamed to note).

\RequirePackage{filecontents}
\begin{filecontents}{rahm.bib}
@misc{cnn2011rahm,
Author = {{Editor CNN}},
Date-Added = {2013-11-21 09:15:03 +0000},
Date-Modified = {2013-11-21 09:26:00 +0000},
Howpublished = {\url{http://edition.cnn.com/2011/POLITICS/01/27/emanuel.ballot/}},
note = {Last checked on Nov~01, 2013},
Month = {January},
Title = {Illinois {Supreme Court} keeps {Emanuel} on ballot},
Url = {http://edition.cnn.com/2011/POLITICS/01/27/emanuel.ballot/},
Urldate = {Jan 28, 2011},
Year = {2011},
}
\end{filecontents}
\documentclass{article}
\usepackage{natbib}
\bibliographystyle{apalike}
\usepackage[hyphens]{url} % <-- new
\begin{document}
\noindent
\cite{cnn2011rahm} reports that \dots
\bibliography{rahm}
\end{document}
jss2style available on CTAN. – Paul Rougieux Jan 02 '17 at 23:17