It depends more on the complexity of the call then on id vs. selector, see google docs.
As the browser parses HTML, it constructs an internal document tree
representing all the elements to be displayed. It then matches
elements to styles specified in various stylesheets, according to the
standard CSS cascade, inheritance, and ordering rules. In Mozilla's
implementation (and probably others as well), for each element, the
CSS engine searches through style rules to find a match. The engine
evaluates each rule from right to left, starting from the rightmost
selector (called the "key") and moving through each selector until it
finds a match or discards the rule. (The "selector" is the document
element to which the rule should apply.)
So it doesn't need to search the DOM to apply the style, the reverse actually happens. As the DOM is being build the style sheets are being searched for matches. If the above is true, a class will the same rendering speed as an id.