Landing an appearance by the president seems to be a game-changer at least for one show in late-night television. On Monday night, President Barack Obama lifted David Letterman to his most-watched 'Late Show' in four years, with a total of 7.218 million viewers. That was more than enough to propel Letterman, on CBS, past his late-night rival on NBC, Conan O'Brien, in every audience category for the first time since O'Brien became host of the 'Tonight Show' in June. It also gave Letterman a bigger audience Monday than his longtime rival Jay Leno, whose new prime-time hour on NBC hit its lowest number to date, with 5.81 million viewers. (Leno can still claim precedence in one area, however. When he was still host of 'Tonight' and Obama made the first late-night appearance by any sitting president last March, Leno attracted 14.6 million viewers.) O'Brien wound up with 2.44 million viewers, his second-lowest total to date. In all the audience categories where he has beaten Letterman every night, he trailed Monday. Obama's appearance also helped deliver viewers to the program that follows Letterman, 'The Late Late Show,' hosted by Craig Ferguson. Ferguson attracted his biggest audience ever, with 3.24 million viewers. He beat his NBC competitor, Jimmy Fallon, by more than 2 million viewers, and outdrew him in every audience category. (He even topped O'Brien in viewers by almost a million.) As for Leno, he experienced a somewhat predictable falloff now that he is facing full first-run competition from two other broadcast networks. Leno finished third at 10 p.m., well behind the CBS hit drama 'CSI: Miami' and the far-from-hit ABC drama 'Castle.' 'Miami' had 14.2 million viewers and 'Castle' had 9.27 million. Leno also dropped Monday in the 18-to-49-year-old audience NBC cares most about, to a 1.8 rating. ('Miami' had a 4.3 and 'Castle' a 2.3 in that category.) NBC has maintained that any number above a 1.5 will be more than enough to produce big profits because of the lower cost of Leno's show compared with expensive scripted dramas. Meanwhile, in the rest of prime time on Monday, a two-hour premiere of the Fox drama 'House' was the big winner. 'House' scored a 6.7 in the 18-to-49 group and attracted 17.1 million viewers. The most-watched show of the night was 'Dancing With the Stars' on ABC (featuring Tom DeLay doing the cha-cha), which averaged 17.79 million viewers. But that was down significantly from the opening night last season, when 'Dancing' drew 21.35 million viewers. For CBS the best story in prime time was the result for the comedy 'The Big Bang Theory,' whose move to 9:30 p.m. paid off when it hit its best numbers ever. Last season the show was seen at 8 p.m. It scored the best 18-to-49 number of the night for CBS, with a 4.7, improving on the hit comedy that plays right before it, 'Two and a Half Men.' In total viewers, 'Big Bang' had 13 million. 