Iowa, with its sprawling wheatfields and sleepy Bridges Of Madison County aura, is the spiritual and geographical hub of the United States. It might lie at the heart of the country, but it would hardly be expected to figure at the heart of the nation's political life. Nevertheless, the most important phone call received by New York mayor Rudolph Giuliani on the morning after his headline-grabbing triumph at the city's polls came from Des Moines, Iowa's capital. The chief of Iowa's Republican Party apparatus called Mr Giuliani to ask if he would visit the state. And even though two prominent party movers, Jack Kemp and former vice-president Dan Quayle, also called the same morning to offer their congratulations, it was the Iowa call which must have had the mayor's pulse racing. In a presidential-election season, Iowa is the first state to hold party caucuses (or primaries) for the respective nominees, and as such is the unofficial launching pad for White House wannabes. A visit there even three years in advance is enough to set alarm bells ringing in the media. Mr Kemp, Mr Quayle and other Republican hopefuls for 2000 have already been there this year, but even if Mr Giuliani's only link to the state so far was over the phone, it was just as symbolic. 'We want him to get a feel for the state and see if he would enjoy running for president in the year 2000,' local party spokesman Aric Kahle said. 'We just want to see if he can connect with the voters.' That Iowa's Grand Old Party grandees should think it fit to issue the invitation was telling, but it was only the latest swell of a growing wave gently sweeping Mr Giuliani towards a shot at the Big One. If the 53-year-old mayor, who was born and bred in Brooklyn and has worked in New York all his life, wants to know what it would feel like to relocate to the political swamp of Washington, New York magazine last week attempted to provide the picture. Its cover illustration showed Mr Giuliani dressed as George Washington, and asked the question: 'How Far Can Rudy Go?' Now Mr Giuliani has been elected for a second (and, by law, final) term to the toughest mayoral job in the US, that question is on the lips of every political pundit in America. There are several reasons why the question even needs asking. Firstly, the feisty, uncompromising politician has noticeably failed to nip in the bud the rampant speculation that he will run for higher office, and has refused to guarantee that he will serve out his four-year term in City Hall in full. Then there is the factor of the man's own ambition - large by anyone's standards, and with an ego to match. And that ambition and ego have only been stroked by his first term in office, one of the most astonishingly productive tenures in recent political history. The fact that, in a fiercely liberal city where registered Democrats outnumber Republicans by five to one, Mr Giuliani could have turned a narrow 1993 win into a near landslide in 1997 (capturing a quarter of all Democratic voters) speaks for itself. If that were not enough to capture the eye of national Republican kingmakers, his record certainly would: crime down by over 40 per cent, transforming the city where it used to be a suicide bid just to ride the subway into one of the nation's safest; the local economy metamorphosed from bust to boom; run-down areas like Times Square revitalised from centres of sleaze into gleaming tourist-friendly neighbourhoods; and restoring a general sense of civic pride. In short, New York is no longer the fiscally (and morally) bankrupt nightmare of the 1970s and 80s, when union mobsters controlled the strings of government and rubbish littered the streets for weeks. If anything, Mr Giuliani has been the right man at the right time. He launched his political career as district attorney, carving out his tough-guy reputation by taking on the mafia's hardest crooks, including John Gotti and the Gambino clan. If that reputation did not bring him the mayor's job in 1989 (when he lost to Democrat David Dinkins), it was definitely what weary voters were looking for four years later - and he delivered. Many of his achievements have been won by adopting a take-no-prisoners approach to problems, whether it be cleaning mobsters out of some of New York's key businesses, such as the central fish market and convention centre, or revamping the city's sprawling, formerly unmanageable bureaucracy. The negative side of Mr Giuliani (which voters do not appear to care about) is his inability to delegate, his reputedly monomaniacal need for control, and his harsh treatment of colleagues. His first term was mired with disputes and firings of police and schools commissioners. His stubbornness has also often seemed childish, for example his refusal to visit the annual US Open tennis championships in Queens because of a dispute with the organisers over the re-routing of aircraft during the event. Where can he go from here? The first choice could be the White House, but there are others, such as the New York state governorship or the US Senate. Colleagues say he may find the former too much of a sideways move, while others wonder about his desire to be just one of 100 senators, lost in the Washington whirlpool. The seat held by Democrat Daniel Moynihan may become free in 2000, which means Mr Giuliani would have to retire early from City Hall and leave the mayor's job in the hands of a local Democratic official, Mark Green, who would automatically inherit it. But if Mr Giuliani accepts Iowa's ego-stroking invitation and takes a shot at the chance to be the Republican nominee to succeed Bill Clinton, what are his chances? Historically, they are almost nil. A New York mayor has never made it to the White House, let alone the Senate. Only one New York politician, former state governor Franklin Roosevelt, went on to become president. In other words, New York politics appears somehow to exist within its own political time-zone, and its products rarely appeal to voters on a national level. Mr Giuliani is, of course, in a different league, because a tough, crime-busting leader who courts no fools is just as likely to appeal to a Texas farmer as a Bronx cabbie. But his biggest problem may be within his own party. It is now a fact that to secure the Republican Party's nomination for president, a candidate has to stand to the right on enough issues to satisfy the powerful Christian constituency. And while Mr Giuliani may look like a crazed right-winger in a New York context, he is a veritable leftist in the arena of his national party. He is pro-abortion (a big minus), pro-gun-control (a huge minus) and - perhaps the biggest handicap of all - has demonstrated no party loyalty whatsoever. Always eager to be his own man, he backed liberal Democrat Mario Cuomo over his own party's candidate, George Pataki, for New York governor in 1994. When Mr Pataki won, Mr Giuliani refused to eat crow and bickered publicly with the victor for months, alienating many of his party's powerful figures, most importantly Al D'Amato, the widely disliked but influential New York senator who can make or break his colleagues' careers. However, a man with charisma and national appeal could conceivably leapfrog over the party's internal hurdles and win on name-power alone: consider the example of General Colin Powell, who would probably have won the nomination in 1996 had he decided to run. Mr Giuliani could conceivably count on his personal appeal to convince party elders that he has the best chance of beating Al Gore or whoever fronts for the enemy in 2000. 'He's not seen as too New Yorky, like [former mayor Ed] Koch,' said Mitchell Moss, an academic at New York University. 'Rather, Rudy is the man who kicked New York's butt . . . the man who made the place safe for the rest of America.' Moreover, the Republican Party is a blank slate, with no obvious candidates for the prime position. But if Mr Giuliani is to eschew running for the presidency, or fail during the nomination process, tongues are wagging to the effect that he will make a great vice-presidential running mate. For a conservative Republican, he would provide a more moderate but tough East Coast appeal, while for a Democrat like Mr Gore (yes, the suggestion has been floated) his tough persona would help bring in conservative types undecided about voting Democrat again. Whether such a concept can work is another matter. A notorious control freak, the prospect of Mr Giuliani having to grit his teeth as the nation's perennial number two is difficult to imagine. Al Sharpton, a New York black community leader, put it wryly in a comment to New York magazine. 'I pity the guy who takes Rudy for vice-anything,' he said. 'He'll need a food taster.' One more question mark of a personal nature hangs over Mr Giuliani's future ambitions. His marriage to local TV broadcaster Donna Hanover appears to be on the rocks - a rumour bolstered by her staying at home rather than joining him at his victory rally on Tuesday night. Their relationship appears to have suffered under speculation (probably unfounded) that he has been having an affair with his closest lieutenant, press aide Cristyne Lategano, and Ms Hanover may only be avoiding filing for divorce in her husband's political interests. But then again, a White House candidate had a similar problem in 1992. His name was Bill Clinton.