Polls and election results over the last week reminded Americans that politics seldom moves in a straight line. As in physics, action produces reaction. Overreach invites backlash.

For a long while former President Trump and his cronies seemed to be immune from this rule of political life and from the consequences of even the most outrageous conduct. As Trump himself once famously said, “I could stand in the middle of Fifth Avenue and shoot somebody and I wouldn’t lose voters.”

And so it seemed. He escaped conviction in not one but two impeachment trials and cowed Republican leaders to fall in line after the January 6 insurrection. He remains the leading contender for the Republican party’s 2024 presidential nomination.

Today Republicans are still falling over themselves to prove their loyalty to him by outdoing each other in extremism.

On 19 August, a Republican candidate for Florida’s state assembly even took to Twitter to call for violence against federal law enforcement officials. “Under my plan,” Luis Miguel tweeted, “all Floridians will have permission to shoot FBI, IRS, ATF and all other [federal agents] ON SIGHT! Let freedom ring!”

In Washington, the US supreme court cast aside almost 50 years of settled precedent to overturn Roe v Wade. Republican-dominated state legislatures rushed to enact draconian restrictions on women’s reproductive rights.

This kind of extremism may be off-putting to swing voters. There are signs that most Americans aren’t ready to trade their rights and freedoms for a strongman and his election-denying, rights-infringing, violence-threatening allies. As the Cook Report’s Amy Walters wrote on 26 August: “The more Trump is in the news, the more dangerous the political climate for the GOP.”

But let’s start with the supreme court’s Dobbs decision.

Dobbs sent shock waves across the political spectrum and has jolted Democratic turnout. On 25 August, Axios reported that immediately after Dobbs, “Democratic primary turnout for governors’ races increased … in five of the eight states holding contested primaries.”

Similarly, a report from TargetSmart suggests that in states like Michigan and Wisconsin “where reproductive rights are at stake”, women “are out-registering men by significant margins.”

This pattern portends a “pink wave” in November, as women mobilize to defeat pro-life candidates. We saw evidence of this in the 23 August special congressional election in New York, where Democrat Pat Ryan defeated Republican Marc Molinaro, 52% to 48% in a bellwether swing district.

Ryan’s campaign message was largely focused on protecting abortion rights. His victory follows the striking 2 August referendum vote in Kansas, where voters overwhelmingly rejected an attempt to ban abortion.

Are Republicans being taught a lesson they should have learned from history?

When the supreme court gets too far out in front of – or too far behind – the American public by ignoring American sentiment, political backlash results. That happened in the 1850s in the run-up to the civil war and in the 1930s when the conservative court that Franklin Roosevelt inherited struck down a new minimum wage law.

It happened again after Roe v Wade, when abortion foes reacted and organized for a 50-year battle that resulted in a reactionary court majority.

Republicans may now be reaping what those reactionaries on the court sowed.

And it isn’t only that many Americans have been alarmed and aroused by what the court did last June. They are also awakening to the threats posed by Trump’s “big lie” and the election denial it has inspired.

Democratic messaging that has called out the “big lie”, along with the meticulously presented hearings of the January 6 congressional hearings, seem to be taking root.

Americans are coming to see that, as President Biden has warned, “A poison is running through our democracy … with disinformation massively on the rise. But the truth is buried by lies, and the lies live on as truth.”

At the start of this summer’s January 6 hearings, Republican congresswoman Liz Cheney echoed that sentiment: “People must pay attention. People must watch, and they must understand how easily our democratic system can unravel if we don’t defend it.”

An NBC News poll last week suggests that the American people are indeed now paying attention. It found that more respondents ranked “threats to democracy” as the most important issue facing the country, more important than inflation or jobs.

Other polls suggest that candidates who are running as election deniers or opponents of a woman’s right to choose will pay a price in November.

Take Pennsylvania, for example. A Franklin & Marshall poll released on 25 August found that the Democratic candidate for the Senate, John Fetterman, is leading Trump-endorsed election denier Mehmet Oz, 43% to 30%. Fetterman is also a vocal abortion rights supporter, while Oz supported overturning Roe.

The same poll also shows that the Democratic candidate for governor in Pennsylvania, Josh Shapiro, leads the Trump favorite and abortion foe, Republican Doug Mastriano, by 44% to 33%.

According to the Washington Post, “In 2020, Mastriano tried to block Pennsylvania’s certification of Biden’s victory by introducing a resolution asserting incorrectly that the Republican-dominated legislature had the right to choose which electors’ votes should be counted.” As the Post also notes, “He attended the Jan. 6 riot … where he was captured on video crossing the police line.”

This is not to say that in Pennsylvania or elsewhere the Trump fever has completely broken. And polls are not the same thing as an election. But they are signs of hope.

Democracy won’t save itself. Abortion rights will not restore themselves. The American majority’s power to defeat Trumpism lies at the ballot box. If Trumpist candidates lose in general elections, over time Republicans may get the message that they’ve placed a losing bet on extremism.

There is much to be done by Americans committed to preserving our republic and to saying “no” to Trump. As former president Obama put it in his 2017 farewell address: “It falls to each of us to be … jealous guardians of democracy.” Across America, a majority of voters are ready to do just that.

• Austin Sarat is a professor of jurisprudence and political science at Amherst College and the author of Gruesome Spectacles: Botched Executions and America’s Death Penalty

• Dennis Aftergut is a former federal prosecutor, currently of counsel to Lawyers Defending American Democracy