Let’s look at the three cases we have of presidential impeachment. Both Bill Clinton and Andrew Johnson were impeached by the House of Representatives, though not ultimately voted to be removed by the Senate. You could consider these the “failed” impeachments. We also have Richard Nixon, who resigned before he could be impeached and removed, which he almost certainly was going to be.
Clinton seems to be poster boy for this, so we’ll begin with him. Formal impeachment proceedings were launched against Clinton in 1998. Clinton was halfway through his second term, which he had won handily by 8.5 percentage points. His impeachment moved incredibly fast by government standards, and lasted only from October 1998 to January 1999. For comparison, the third season of Buffy the Vampire Slayer in 1998/1999 ran longer than Clinton’s impeachment hearings.
The impeachment had just started when the 1998 midterm elections were held. Whether they should count or not because of that is a personal opinion. For what it’s worth, this election was the first midterm since 1934 where the president’s party picked up seats in the House of Representatives (5), though Republicans retained control of both chambers.
A better example is probably the 2000 elections. Clinton obviously wasn’t running as he had completed two terms, but Vice President Al Gore was. Gore went on to lose the race to George W. Bush by one of the smallest margins in U.S. history, but one way or the other Republicans took control of the White House two years after their “failure.” They also narrowly held control of the House by just three seats, and only held control of the Senate thanks to the tiebreaker vote of Vice President Dick Cheney. Democrats did okay in 2000, but it was not enough to get a majority. Instead, the Republicans would hold the reins of power. Once the 9/11 attacks happened, Bush and the Republicans were able to ride a wave of public sentiment that carried them to further victories in the 2002 midterms. If there was some sort of backlash to trying to impeach Clinton that cost the Republicans federal power, I fail to see it.
Nor are there any particular answers to be found in the tale of Johnson. It is true that Johnson was a Democrat, but he was also the unity ticket vice president with Republican Abraham Lincoln. He was never elected president in his own right as a Democrat and only ascended the office because of Lincoln’s assassination.
Johnson’s impeachment was even faster than Clinton’s, lasting from February to May of 1868 and finished in plenty of time for the 1868 elections. However, those elections are also impossible to judge by modern standards. Six former Confederate states were re-admitted to the Union in 1868 and 1869. The Republicans improved on their overwhelming majority in the Senate and House thanks to the fact Republicans controlled most of the power in the Reconstruction states. Ulysses S. Grant won by 5.4 percentage points over Horatio Seymour. Johnson couldn’t even secure the nomination for his own party to try.
The Republicans had near total control of the country after the Civil War. The Democrats were able to retake the House in 1874/1875 thanks in part to reports of incredible corruption in the Grant administration and an economic depression. The Democrats would finally retake the Senate in 1878/1879, and the White House in 1884.
Johnson was virtually a lone operator who barely had a party to be in control of since most of its members had seceded from the Union. That power base slowly came back, though it wouldn’t fully recover until well into the 20th century. What the impact of Johnson’s successful impeachment but failed removal would have been in a more normal era is anyone’s guess, but it has no bearing on what we’re going through now.
Last, it’s worth considering Nixon. Nixon’s impeachment began in 1973, one year after Nixon had won re-election in a landslide. It lasted until his resignation in August 1974. How did the Democrats do in that midterm?
Pretty well. When the dust cleared the Democrats had 61 seats in the Senate, further securing their control. They also routed the Republicans in the House, gaining 49 seats. They would go on to reclaim the White House in 1976 when Jimmy Carter beat Gerald Ford. Granted, most people would consider Nixon’s resignation a successful impeachment in practice if not by letter of the law. Perhaps the Democrats were supposed to win out of all of that.
However, whether a removal process worked or not, in all three cases we have the president suffered mightily. None won re-election, none of their successors triumphed, and in no case did their party manage to retain or take control of Congress. Formal impeachment proceedings appear to spell doom for the president’s party going by the historical record.
That’s not to say they will this time. Trump is an anomaly in American presidential history in many ways, and expecting even his impeachment to go according to precedent is probably asking too much of this weird, shattered timeline. That said, to the extent that you can judge from previous impeachments a failure to remove from office only seems to help the accusing party gain and hold power. The backlash narrative is a myth not supported by a hard look at elections immediately after impeachments were held. It's likely born out of the belief Clinton's impeachment was a sham. Maybe it was, but sham or not the Democrats would take eight years to recover any real power.