Could Angus Robertson, the SNP's Westminster leader, be a kingmaker after the next Westminster election, deciding whether Gordon Brown or David Cameron is installed in Downing Street?

That is what his party leader, Alex Salmond, invited us to contemplate at his party's spring conference at Heriot-Watt University yesterday.

The notion is based on two propositions. One is that the polls suggest a stronger-than-usual chance that Labour and Conservative could be close run, and that the LibDems risk losing ground. If either of the dominant parties need support, they are going to have to do deals, and the LibDems are not the only potential suitors. The SNP or Northern Irish votes could become crucial. That reflects the other proposition: that the SNP grows from its current six seats to Mr Salmond's new target of 20.

To be a kingmaker, Mr Robertson, the Moray MP, is opting not to declare whether he would favour a Labour or Tory government. His aim is to use any leverage he has to get benefits for Scotland. Indeed, there is a school of thought that an English-dominated Conservative government would not only have to concede its lack of authority in Scotland and give ground on the constitution, but that it would be more willing to do so than a Labour Party led by Scots.

Mr Salmond will only publicly discuss hypotheticals based on positive outcomes for him, and the idea of gaining 14 seats at Westminster would be very positive, in light of the result at the last Westminster vote in 2005.

That campaign, with Alex Salmond newly re-installed as leader, was run by the seat of Nationalist pants, winning only 18% of the vote and six seats, behind LibDems on both counts. The party reckons the political landscape and its fortunes have changed. So have those of Labour, which has 40 Westminster seats out of 59, and would be the main target for SNP gains. And LibDems, who surged in 2005 into several second places and 11 seats, have had poor Westminster poll ratings recently, and having lost two Holyrood constituency seats to Nationalists last year, they are on the back foot.

The plan is to protect its six seats, four of them with slight majorities. On paper, only one Labour-held seat is marginal; Ochil and South Perthshire, where Labour's Gordon Banks has a majority of 688. Defence and Scottish Secretary Des Browne is one of the next most vulnerable Labour MPs, but that would still require a 10% vote swing to dislodge him in Kilmarnock and Loudoun.

With Labour on 40 seats, the SNP would require swings of nearly 20% from Labour if it is to get near its target, and it would have to win from third or fourth place in 2005, having been beaten by LibDems in unlikely places like Glasgow and Lanarkshire. There are only 19 seats where the SNP was in second place three years ago. In Argyll and in Gordon, its top LibDem targets, although gains at Holyrood last year, the SNP came fourth in 2005.

So a successful SNP strategy has to persuade Scottish voters the starting point for ousting incumbents was not Westminster in 2005 but Holyrood elections last year, when it secured 21 out of 73 constituencies. In those, Nationalists successfully dislodged Labour from seats where it had been building support, such as Glasgow Govan, Livingston, Western Isles and Central Fife.

It gained in some surprising places, such as Edinburgh East, Stirling and Cunninghame North, while Labour hung on in seats such as Cumbernauld and Kilsyth. While the SNP is not making its target list public, all these are likely to feature.

SNP strategists reckon their aim of winning at least 20 seats is based on hard canvassing data, showing that those who switched to the last year are willing to stick with the SNP for Westminster.

They are stepping up their efforts with "a month of action", street stalls, a million "Vision" leaflets, and newsletters highlighting the council tax freeze. The campaign is to show continuity from what worked last year, linking through to the European elections next summer, the Westminster election expected in 2010, Holyrood a year later, and councils pencilled in for 2012.