US President Joe Biden was last week hit with a nasty double whammy: the launch of an impeachment inquiry in the House of Representatives and the indictment of his son, Hunter. The impeachment inquiry may ultimately prove less of a headache. This is hardly the first such probe, but it is the only instance in which the House has launched one on the basis of no evidence. No break-ins and erased tapes. No blue dress. No shaking down of foreign leaders. No assault on Congress. Nothing. After House Speaker Kevin McCarthy announced that he had unilaterally created the inquiry – after months of vowing never to do so without a vote of the full House – Republicans struggled mightily to explain its rationale. Representative Nancy Mace, in particular, gave numerous TV interviews in which she insisted that there was ample evidence of bribery or corruption associated with Mr Biden, but was unable to point to anything in particular. Asked by CNN's Kaitlin Collins if such an inquiry didn't need to be based on evidence, Ms Mace gave the game away by replying, “Well, that’s what the inquiry is for. It’s to get more evidence.” Representative Michael McCaul insisted: "We don't have the evidence now, but we may find it later.” That’s highly reminiscent of Donald Trump's attorney Rudolph Giuliani saying to an Arizona official about his own overwrought allegations of fraud in the 2020 election: “We’ve got lots of theories. We just don’t have the evidence.” The impeachment push against Mr Biden is so weak that Mr McCarthy had to be forced to launch it by Republican right-wing extremists. Both the Speaker and many GOP representatives from centrist districts will surely be hoping that whatever hearings and other measures are undertaken, they drag on indefinitely and without much fanfare. Otherwise, there's every danger of a significant public backlash if the country gets the sense that this is baseless, frivolous and partisan, and worse – in part because it's true – that it's simple automatic payback on behalf of the twice-impeached Mr Trump. Republicans have been diligently digging around Mr Biden and his son since last year's midterms and have discovered absolutely nothing directly connecting the president with the financial dealings of his formerly drug-addicted adult child. It's largely been a campaign of innuendo, elaborating unproven criminal or unethical dealings, apart from the younger Mr Biden's evident and unsavoury, but sadly typical, willingness to try to profit from his last name. Right-wingers then suggest that the President must have also been involved in dealings that were not merely unsavoury or even unethical but downright illegal. Based on this chain of groundless implications, they have made a fetish out of the preposterous phrase "the Biden crime family", as if the whole clan is corrupted and constitutes the equivalent of a Mafia gang. This creates a huge contradiction in Republican messaging: Mr Biden cannot simultaneously be the mastermind controlling a multinational criminal enterprise and a doddering, senile old fool. Their inquiries thus far have not only failed to uncover evidence of any of this, they frequently left Republican congressional leaders looking desperate and foolish. So, unless Mr Biden actually has something to hide, which seems very improbable, he likely has little to fear politically from this impeachment agenda, which is liable to deliver some significant self-inflicted wounds to his Republican adversaries or fade into the background. That's much less true of the indictment and likely upcoming trial of Hunter. The president's son is accused of purchasing and possessing a gun while using outlawed narcotics and lying on a gun purchase form about his use of these controlled substances. He had reached a plea deal with a Trump-appointed prosecutor that probably would have allowed him to avoid incarceration, but that was thrown out as insufficient by a judge. Because he and his lawyers continued to insist that the plea deal was binding, he has been indicted. In a rational world, being patiently faithful and forgiving of the foibles of a wayward and drug-addicted child wouldn't be considered a stain on any parent's character. Hunter Biden, after all, has never run for or held office, or occupied any government position, and even Republicans don't suggest Mr Biden was responsible for his son's drug use or alleged gun violations. Indeed, the strident protection of gun ownership with few restrictions by the ultra-conservative present Supreme Court may provide Hunter's legal team with their most potent arguments. But politics is rarely rational. Mr Trump and his followers claim the gun charges were brought precisely because the president is obviously not involved in them while implying more serious charges were avoided because they could have implicated Mr Biden. None of that is based on any evidence either. Still, many Americans may gather over the next 14 months before the 2024 election that Mr Trump is on trial for something or other, and so is Mr Biden's son, and therefore there is some kind of equivalency. The fact that the charges brought against Mr Trump and Hunter Biden are essentially on opposite ends of the spectrum of nonviolent criminal offences – with the former president facing some of the most serious imaginable accusations and the incumbent’s son accused of minor technical violations of the law – may be lost on a great many people, even those who don't depend on Fox News for current events consumption. Some anxious Democrats are renewing their appeals to Mr Biden not to run for re-election, citing his age and the fact that he is currently running neck and neck with Mr Trump in polls. His supporters retort that Mr Trump is nearly as old, and frequently makes rather less sense when speaking in public, and that virtually every first-term president is in relative polling parity against hypothetical opponents a year out from re-election. Yet the indictment of his son is a genuine headache as well as heartache for the President. It will deprive Republicans of plausible claims that Hunter is receiving preferential treatment from the Justice Department, but it sets up a potential, albeit entirely invalid, offset to Mr Trump's own coming trials. Still, with inflation down and GDP up, plus an impressive string of domestic legislative and foreign policy successes, Mr Biden still seems on course to win a second term, although most Americans, including most Democrats, would prefer someone younger. He certainly wouldn't want to change political, let alone legal, positions with Mr Trump.