The week after the first presidential debate, with Mitt Romney riding a surge in the polls, Lorne Michaels believed he was close to achieving one of the perennial objectives of an election year for the celebrated television show he created and still produces, “Saturday Night Live.”

Landing a presidential nominee as a guest.

The excitement at the show about a possible walk-on by Mr. Romney was tangible. But sometime that Friday, interest from the Romney camp cooled; the Republican candidate did not follow the precedent set in other recent presidential races by John McCain and George W. Bush by appearing on television’s most famous address for political satire.

A deal with the Romney camp has not been as close since, though Mr. Michaels said he is keeping offers open to both campaigns for a last-second appearance. That happened four years ago when Mr. McCain appeared as a guest three days before Election Day, performing a memorable sketch with Tina Fey as Sarah Palin, spoofing a home shopping appearance in a late appeal for cash.

Mr. Michaels is hardly alone in his pursuit: every other late-night television producer has been chasing Mr. Romney for weeks to try to secure a guest appearance, with no success so far. Mr. Romney also has declined invitations from a host of other media outlets who have landed President Obama for interviews, including MTV and NBC News, which was given two days of access to the president during his campaign tour last week.