In interviews, Republicans who went to the rally or who have followed Ms. Greene and Mr. Gaetz from afar said the pair’s efforts should not be discounted. In 2016, Mr. Trump stormed through the Republican primary and swept to power after party leaders underestimated the grass-roots appetite for his openly anti-immigrant language, his insults toward G.O.P. leaders and his economic message that targeted some corporations.

Now, Mr. Gaetz and Ms. Greene appear intent on doing the same thing, to set the table for another presidential run by Mr. Trump or to send a warning shot to any would-be successors.

If their bet is correct and the Republican base has left the Trump era wanting more of his bombastic style, it will have profound effects on the country’s political landscape. At minimum, Trump loyalists have shown themselves to be a stubborn force, threatening to pull additional congressional and presidential candidates into the waters of misinformation and racial intolerance.