No, PEG is prone to exactly this in its default form. Parser combinator usually means something PEG-ish anyway.
If you memoize (packrat), it improves to polynomial time (not sure what, but it's not linear; that's false advertising and a fraudulent claim), but you're still stuck with the vulnerability to bugs in the grammar.
A better idea is to create a parser-combinator-style API on top of an LL or LR backend, for guaranteed linear time and only enough stack space for the deepest part of the AST.
If you memoize (packrat), it improves to polynomial time (not sure what, but it's not linear; that's false advertising and a fraudulent claim), but you're still stuck with the vulnerability to bugs in the grammar.
A better idea is to create a parser-combinator-style API on top of an LL or LR backend, for guaranteed linear time and only enough stack space for the deepest part of the AST.