Can an html element have multiple ids?

Contrary to what everyone else said, the correct answer is YES

The Selectors spec is very clear about this:

If an element has multiple ID attributes, all of them must be treated as IDs for that element for the purposes of the ID selector.Such a situation could be reached using mixtures of xml:id, DOM3 Core, XML DTDs, and namespace-specific knowledge.

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Edit

Just to clarify: Yes, an XHTML element can have multiple ids, e.g.

<p id="foo" xml:id="bar">

but assigning multiple ids to the same id attribute using a space-separated list is not possible.

No. While the definition from W3C for HTML 4 doesn't seem to explicitly cover your question, the definition of the name and id attribute says no spaces in the identifier:

ID and NAME tokens must begin with a letter ([A-Za-z]) and may be followed by any number of letters, digits ([0-9]), hyphens ("-"), underscores ("_"), colons (":"), and periods (".").

No. From the XHTML 1.0 Spec

In XML, fragment identifiers are of type ID, and there can only be a single attribute of type ID per element. Therefore, in XHTML 1.0 the id attribute is defined to be of type ID. In order to ensure that XHTML 1.0 documents are well-structured XML documents, XHTML 1.0 documents MUST use the id attribute when defining fragment identifiers on the elements listed above. See the HTML Compatibility Guidelines for information on ensuring such anchors are backward compatible when serving XHTML documents as media type text/html.