The leadership of the Republican Party is set to push through strict new rules slashing the number of televised primary debates for the 2016 presidential race as part of a wider and increasingly blatant strategy to weaken the sway in its ranks of the Tea Party, which is seeing its popularity fade.

The expected vote by members of the Republican National Committee (RNC) at their annual meeting in Memphis, Tennessee, to at least halve the number of debates and thus make it harder for fringe candidates to gain air time is just the latest sign of a push by the establishment wing to gain the upper hand in the intra-party civil war that has been raging since 2010 when the Tea Party burst on to the political scene.

It comes as huge quantities of money and time are being invested in stopping far-right conservatives from gaining traction in competitive seats across the country as the Republicans seek to gain control of the US Senate and bolster its numbers in the House of Representatives in November’s mid-term elections.

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That the influence of the Tea Party may have peaked is highlighted in a new Gallup Poll. It finds that only 41 per cent of registered Republicans and Republican-leaning independents now support the movement. A Gallup poll in 2010 showed 61 per cent of registered Republicans calling themselves Tea Party supporters. Among all voters, backing for the movement dropped 10 points since 2010 from 32 per cent to 22 per cent.

Meanwhile a first round of primary votes held earlier this week offered little encouragement to Tea Party activists. Most strikingly, a Senate nomination battle in North Carolina saw establishment candidate Thom Tillis, currently the state House speaker, easily outrun his challengers from the right, in part thanks to infusions of cash from the national party that paid for television advertising.

The victory of Mr Tillis was the first fruit of a national strategy by the RNC to stifle the chances of right-wing firebrands who threaten to win primary races but whose chances of actually taking seats in Congress in November appear dim. The party is still stinging from the humiliations of 2012 when the party squandered opportunities to take key Senate seats because of candidates who were too far on the fringe.

Protecting sitting establishment Republicans from primary challenges from the right wing is also a top priority. The wagons may already have been successfully circled around Mitch McConnell, the Minority Leader in the Senate.

Facing re-election in Kentucky, he now seems set easily to see off conservative firebrand Matt Bevin, whose platform includes the re-introduction of cock-fighting.

The RNC vote in Memphis will approve limiting to 10 or fewer the number of media-sponsored debates during the 2016 presidential primaries, down from 20 in 2012. The changes were dressed up today by Reince Priebus, the RNC chairman, as an effort to take control of the primary process away from the “liberal media” outlets that are the debate hosts. “Our candidates deserve a fair hearing,” he told members. “Our voters deserve a real debate. And the liberal media doesn’t deserve to be in the driver’s seat.”

However, they are clearly also designed to accelerate the winnowing out process so the eventual nominee emerges much faster. It was that endless string of debates in 2012 that sustained the campaigns of the likes of Michele Bachmann, Herman Cain and Newt Gingrich, who were all favoured by the Tea Party, last time.

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And it is memories of the mauling suffered by Mitt Romney from his primary rivals that are also driving the RNC to bring forward the dates of the 2016 Republican Party convention to early summer instead of late August or early September as would be traditional.

This is also meant to protect the nominee from being distracted by – and dragged to – the right and ensure all energy is saved for attacking the Democrats.

“We can’t expect to win if we are fighting each other all the time,” Matt Borges, chairman of the Ohio Republican Party, said. “It makes sense to get control of the process.” In theory, any candidate who flouts the new rules by, for example, agreeing to take part in an off-the-books public debate, will be barred from taking part in any other official debates and stripped of delegates for the national convention.

There is plenty of reason to doubt the workability of the rules, however. If one candidate bolts and agrees to attend a rogue debate, it is unlikely that his or her rivals will feel able to stay away. Meanwhile the new muscle-flexing by the RNC risks triggering an angry backlash from the Tea Party, which is founded on distaste for centralised power and control.

And while the Tea Party may be a diminishing force it certainly is not a spent one. Indeed, even if its candidates fall short in many primary contests this year and perhaps in the 2016 presidential derby that does not mean their presence on the ballot won’t continue to move the debate and the party at large in their direction.

“We organise grassroots to change the behaviour of the people already in office,” noted Matt Kibbe, whose FreedomWorks political action committee has been active trying to thwart Senator McConnell in Kentucky. “That’s the whole point of participating in the primary process.”