Americans voted overnight in primary elections in four states and one congressional by-election, and this morning as results come in they are being eagerly watched for pointers to the likely direction of mid-term elections in November.

Two Democrat senators up for re-election this year, in Pennsylvania and Arkansas, are being challenged in the primaries, and both sides’ nominees for the Republican-held state of Kentucky are being selected. (Oregon is also holding primaries, but they are less controversial and being on the west coast its results won’t come through until mid-afternoon Australian time.)

No-one really thinks the Democrats could lose control of the Senate in November, so apart from the fate of individual senators, the main interest in today’s races is what they say about the mood of the country: specifically, whether they show the sort of swing to conservative and/or anti-establishment candidates that could deliver Republicans a majority in the House of Representatives.

The first race decided — for the Republican Senate nomination in Kentucky — could hardly be more emblematic. It was an easy win for Rand Paul, a leader of the “tea party” movement and son of perennial Republican outsider Ron Paul, who defeated Kentucky’s secretary of state Trey Grayson, the favorite of the party’s establishment.

Paul’s politics are avowedly libertarian — low tax, small government, and personal freedom (his father has been a long-time supporter of drug legalisation, not otherwise a popular conservative cause) — but with a strongly nativist streak. While the tea partiers mostly talk about economics, the demons of racism, misogyny and anti-Semitism never seem to be far behind. The Kentucky result suggests that those forces are now to the fore in the Republican party.

But the danger of insurgent victories at the primary level is that they can saddle the party with a more unappealing candidate in the general election. Kentucky is a reasonably safe Republican state — GOP Senate leader Mitch McConnell is its other senator — but Democrats will be targetting Paul’s non-mainstream views. The Democrat nominee looks like being state attorney-general Jack Conway, who is holding onto a narrow lead over lieutenant-governor Dan Mongiardo.

In Pennsylvania, early results are less decisive. The Republican Senate nominee will be former congressman Pat Toomey, but he will face either incumbent Democrat Arlen Specter — who started out as a Republican but switched parties last year — or his challenger Joe Sestak, who appeals to his party’s more liberal wing. Pre-election polling showed Specter narrowly trailing, and although early figures were encouraging for him they came chiefly from Philadelphia, his strongest area; Sestak has now almost overtaken him and will probably go on to take the nomination.

Another sitting Democrat, Arkansas’s Blanche Lincoln, is also in trouble from a liberal challenger (or at least as liberal as you get in Arkansas) – current lieutenant-governor Bill Halter. Lincoln is unpopular with the grassroots for having opposed Barack Obama’s health care reform; nonetheless, very early returns show her ahead, although unexpectedly strong support for a third candidate could force a runoff.

Although one might assume that the more centrist Democrat incumbents would have a better chance in November, Nate Silver at argued that the polling evidence shows otherwise: that while Republican insurgents were something of a liability to their party, the Democrat challengers were polling better than the incumbents against their likely Republican opponents. It will be very interesting to see if that holds up for the rest of the year.

The other closely-watched contest is a House of Representatives by-election for the 12th district of Pennsylvania, vacated by the death of long-term Democrat John Murtha. Republicans had some hopes of snatching the seat, but with about 10% of precincts reporting, Mark Critz is holding a comfortable lead for the Democrats.