The other day I speculated on how the tide again seemed to be running against capital punishment in the United States, after a long period in which it enjoyed overwhelming popularity. Now there’s a story in this week’s New Republic suggesting that conservatives might be coming around to the cause of abolition.

The author, Lydia Depillis, reports from the annual Conservative Political Action Conference (CPAC) on the debut of a new group, “Conservatives Concerned About the Death Penalty”, which she says “say they’ve found a warm welcome.” “Many people in the exhibit hall that afternoon agreed that the death penalty—when described as the purest manifestation of state power and free spending run amok—had probably outlived its usefulness.”

There’s no doubt that part of the story about the death penalty’s fortunes in the last few decades has to be told in partisan terms. Democrats have been divided on the issue, with both prominent supporters and prominent opponents, but Republicans have been almost unanimous. When Maryland’s legislature voted last week to end capital punishment, only two of the 43 Republicans in the lower house voted in favor.

If Republicans, and conservative Republicans in particular, do start to move on this issue it will be a significant breakthrough.

But the Republican Party has to try something. Its voter base is becoming less and less representative of the nation at large, and its economic policy, on which its leaders have staked most of their political capital, is horrendously unpopular. Long years in the wilderness loom unless it can change tack.

So far, the most popular suggestions involve taking more liberal positions on immigration and possibly same-sex marriage – issues that might broaden the party’s appeal with such key demographic groups as Hispanics and young people. To some extent, flexibility on capital punishment would be the same sort of thing. As Depillis points out, it can also be sold to budget-cutters, since “tough on crime” measures almost invariably turn out to be more expensive.

But it’s also part of a more general – and more controversial – option for realignment in the Republican Party. That option is associated in particular with Rand Paul, senator from Kentucky and son of perennial outsider candidate Ron Paul. Paul junior made headlines earlier this month when he engaged in an old-fashioned filibuster for more than twelve hours against the nomination of John Brennan as CIA director, largely in protest against the administration’s assertion of its right to kill American citizens without trial.

At CPAC, Rand Paul was the winner of the straw poll of likely presidential nominees, narrowly ahead of Marco Rubio but well clear of other contenders. Of course his father won the straw poll twice, in 2010 and 2011, and it never did him much good.

What most marks off the Pauls, father and son, from the Republican mainstream is their scepticism about military power. They argue for cutting military spending, winding back national security measures like the Patriot Act, withdrawing troops from overseas and reducing if not eliminating the military aid budget.

For years, these positions have been heresy in the Republican Party. By and large they still are. But there are signs of movement: Paul’s filibuster drew support from many mainstream Republican leaders, and the party seems increasingly comfortable with the “sequester” cuts (made semi-permanent this week), which cut military as well as civilian spending.

As usual, a long period in opposition makes a party start to question the desirability of government power in a way that never would have occurred to it while in office. Capital punishment and a whole set of “tough on crime” shibboleths are obvious candidates for the same treatment. But militarism runs deep in the Republican Party’s DNA, so it will be an uphill task.

Paul also faces the predicament of most insurgent candidates. As long as the establishment opposes him, he can’t win the nomination. But if the establishment comes around to his positions, then an establishment candidate will be found to endorse them – in which case most Republican voters will probably prefer them. If Rand Paul and Marco Rubio, say, are both opposing drone warfare and supporting withdrawal from Afghanistan, why would Republicans go for Paul?

Their supporters, and indeed the Pauls themselves, often identify as libertarians, but it’s a curiously limited sort of libertarianism. Opposition to the federal government rarely seems to flow on to more generally anti-authoritarian attitudes. On the contrary, both Pauls have identified themselves with the Tea Party movement, the stronghold of GOP racism, misogyny and anti-gay bigotry.

Republicans were given a more genuinely libertarian choice in last year’s primaries in the shape of Gary Johnson, two-term governor of New Mexico. But Johnson consistently failed to make an impact, suggesting that support for actual libertarianism among Republican primary voters is minimal. Instead he withdrew from the race and ran as the Libertarian Party’s presidential nominee – as had Ron Paul before him, many years ago in 1988.

The Pauls are doing a real service in putting forward ideas that badly need a hearing in mainstream American politics, especially in their opposition to perpetual warfare and the national security state. Unfortunately they may also be doing a disservice by further associating libertarianism in the public mind with “angry old white dude” tea-partyism.

But either way, the broader Republican Party still seems a long way from adopting a generally anti-militarist platform. And even if by chance it does, it’s unlikely that Rand Paul will be its standard-bearer.