Firstly, we have to take into consideration the sheer scale of Beatlemania in the UK in November-December 1963, a couple of months before they appeared on Ed Sullivan. The Beatles were selling enormous amounts of records in the UK; according to Bob Spitz's The Beatles, they sold over half a million copies of the With The Beatles album in the UK on the first day of release, which was unprecedented. A week after the release of With The Beatles, they released the 'I Want To Hold Your Hand' single, which promptly knocked their song 'She Loves You' off #1 in the charts - selling a million copies prior to release - making it the 'fastest-selling single ever released in any market, anywhere', according to Jonathan Gould.

The US can sometimes be a bit inward-looking, shall we say, but 1963 was a time when there was a fair amount of American Anglophilia. British films were popular enough in America in the early 1960s that American studios were funding films made in Britain (notably a series of films with Peter Sellers, and the James Bond films). Similarly, British West End musicals were a fertile ground for Broadway productions in 1963, with Stop The World I Want To Get Off and Oliver! enjoying extended Broadway runs. Tom Wolfe was reporting in the New York Herald about the New York craze for British fashions. In this atmosphere, the Beatlemania in the UK was reported on by the major television news networks in the U.S. (for example). Amidst all of this, Brian Epstein, the Beatles' manager, took a business trip to New York with the aim of getting Capitol to release the Beatles' music.

The Beatles' record company EMI had bought Capitol Records in 1955, and in 1964 it was the largest record company in America. However, Capitol in 1963 continually declined to release the Beatles' new singles. EMI had believed that Capitol knew the American market better than it did, so it didn't overrule them. Capitol's head of International A&R (i.e., the person in charge of releasing foreign music) was one Dave Dexter, who Jonathan Gould describes as a 'crew cut jazz and blue aficionado who had been with the company since the 1940s.' Dexter was part of the culture of Capitol Records, which largely sniffed at rock'n'roll; the only rock'n'roll singer they had on their books during the golden age of the 50s was Gene Vincent. Belatedly, they signed the Beach Boys in 1962 and seems to have considered that enough rock'n'roll for their tastes. Instead, EMI licensed the Beatles' earliest music to Vee-Jay Records and Swan, independent record labels very much without Capitol's reach and power. Vee-Jay had declined to sink their small resources into the Beatles, largely because they were riding high with the success of Frankie Valli and the Four Seasons. (Edit: see /u/rockhistory’s reply to me which complicates the issue of the Beatles being on Vee-Jay and Capitol suing for the rights to the Beatles’ recordings in August 1963, suggesting Capitol’s official disinterest in the Beatles, and the impression relayed to the likes of Brian Epstein discussed below, is not the full story).

Anyway, Epstein had gotten in touch with Ed Sullivan, who was interested because he had flown through Heathrow amidst scenes of Beatlemania as the Beatles returned from dates in Sweden, and so he figured the Beatles would be an interesting act to feature on the program. Epstein's negotiations with Sullivan and his people - to Sullivan's surprise - didn't focus on money at all; the Beatles were effectively paid a nominal fee. Instead, Epstein demanded (and got) 'top billing', an unfamiliar term to Sullivan at the time; he wanted to make sure that the Beatles were the act featured in network advertising for the show. So, Epstein made sure that if you saw ads for the Ed Sullivan show, you saw the Beatles.

With a contract with Ed Sullivan in hand, Epstein went to Capitol in New York, and met with its head, Brown Meggs. Meggs was non-commital during the meeting but a front-page article in the show-business trade magazine Variety in early December seems to have forced his hand (edit: getting the rights to the Beatles’ music back from Vee Jay might have helped too). This article reported the Beatles' astonishing sales in the UK - as Gould puts it, ‘the Beatles had released as many million-selling singles in 1963 as the entire American record industry.' And in a country a third of the sise of the US, no less. This convinced him to not only release the Beatles but to activrly put effort into making them stars. Capitol committed (a very respectable, at the time) $40,000 to publicity of the Beatles, with the plan being to promote a single in January, followed by an album released to coincide with the Ed Sullivan appearance.

This might have been the best money Capitol ever spent on publicity - considering the result! - and included the distribution of stickers claiming 'The Beatles are coming!' (alluding to Paul Revere), and issuing Beatles wigs to sales staff. Then again, maybe they didn't need to spend the money; a disc jockey at a station in Washington DC obtained a British pressing of 'I Want To Hold Your Hand' and began playing it on air, to an immediate listener response, which promptly caused stations in Chicago and St. Louis to begin playing the song, and which was reported on in trade magazines. The release of 'I Want To Hold Your Hand' was brought forward to the last days of 1963 to capitalise on interest in these markets, and Capitol soon began arrangements to press the single in enormous quantities once the real publicity campaign began.

The Beatles entered the Billboard charts with 'I Want To Hold Your Hand' on January 18th, 1964, at #45, and was at #3 the next week. The week after, it was at #1 (the Billboard charts in 1964 had some delay between sales, collation and publishing the charts, too).

By mid-January 1964, the Beatles were already a band that had made the news, with a massive record label push behind them, with a #1 single. And things still snowballed from there. By the start of February, 'I Want To Hold Your Hand' had sold half a million copies in the New York metropolitan area alone (and another million in the rest of the country). By the start of February, the radio station WABC in New York estimated it was receiving 3000 Beatles-related letters a day. So when New York pop radio stations broadcast live from the airport as the Beatles touched down in America, they were not doing so because of any of Capitol's payola - it was simply good business.

The buzz about the band flying into New York led to a large media contingent greeting the band along with the fans; according to a New York Times article from February 8th, 1964, the Beatles were met by 200 reporters and photographers from various media organisations. According to the NYT article by one Paul Gardner,

An official at Kennedy Airport shook his head and said “We’ve never seen anything like this before. Never. Not even for kings and queens.”

In the press conference with those 200 reporters, the Beatles came off as incredibly media savvy and witty. E.g., to quote some of the lines quoted by Gardner:

Mr. Starr was asked what he thought of Beethoven. “I love him,” he said, “especially his poems.”

“Mr. McCartney beamed. “We have a message,” he said. Suddenly there was a moment of silence. “Our message is,” he began, “buy more Beatle records!”

All of this made for excellent TV, and so American news organisations put it on their nightly news programs (for example, here’s NBC’s coverage from that day). So when the Beatles’ first performance was aired on the Ed Sullivan Show on February 9th, Americans had been hearing about these Beatles on the news and in the papers since November. If they listened to pop radio stations, the Beatles were the hot new thing. ‘I Want To Hold Your Hand’ had been #1 for weeks, and was already clearly going to be one of the biggest selling songs of the year. And then the Beatles actually landed in America, and that was covered in the nightly news bulletins of the major TV networks, probably interspersed on one channel in particular with ads for their upcoming Ed Sullivan performance.