This is due to a flaw in the elsart packages. They setup some part counters even though part isn't defined. This confuses cleveref. To fix this, add the following anywhere in your preamble:! TeX capacity exceeded, sorry [input stack size=5000].
Later, you can use cleveref's poorman option to strip all of the cleveref stuff from your document. After that, you can remove this line.\makeatletter \let\cl@part\relax \makeatother
svjour problems: Similarly, if you try combining cleveref with Springer journal support files, you may get this error:
Again, this is due to a flaw in the Springer packages. They setup some chapter counters even though chapter isn't defined. To fix this, add the following anywhere in your preamble:! TeX capacity exceeded, sorry [input stack size=5000].
Again, this can be removed after cleveref's poorman procedure is applied.\makeatletter \let\cl@chapter\relax \makeatother
Source and acknowledgments: The Springer solution was given by "Dan" in a comp.text.tex post. I used it to generate the elsart solution.