Matthew Continetti at The Washington Free Beacon has some thoughts on the question:
History offers clues. The Republican Congress will fight with the president over spending, immigration, the IRS, aid to Ukraine, and the debt ceiling. And it will open investigations into Biden’s personal and professional life.I'm not sure about this, though. The House may wish to impeach Mr. Biden, but it's not so certain that they'd want the Senate to convict and have him actually thrown out of office.
Divided government in a polarized America doesn’t simply halt a president’s legislative agenda. It saps energy out of the executive branch by forcing the White House into a defensive crouch.
Every president since Ronald Reagan has experienced a period of divided government. Every president since Reagan has faced withering scrutiny from an opposition Congress, from a special or independent counsel, or from all the above.
Every president since Bill Clinton has fought Congress over spending. Those battles resulted in at least one government shutdown during three of the past four presidencies. (The Democratic Congress during George W. Bush’s final two years didn’t want to close the government, it wanted to cut off funds for the war in Iraq.)
Reagan was almost impeached for the Iran-contra scandal. George H.W. Bush had to contend with independent counsel Lawrence Walsh and with fallout from the collapse of the Savings and Loan industry.
Clinton’s troubles began with Whitewater, moved on to the White House travel office, progressed to sleazy campaign finance, and climaxed in his impeachment for lying about and covering up his affair with a White House intern half his age.
George W. Bush had to deal with another special counsel investigation, as well as a firestorm over his firing of U.S. attorneys. Barack Obama’s administration was investigated for the Fast & Furious program, IRS targeting of Tea Party groups, and the attack on the U.S. consulate in Benghazi, Libya, on September 11, 2012.
Donald Trump had special counsel Robert Mueller hounding him during his first two years, then Congress impeached him for his unsuccessful attempt to strong-arm the Ukrainians into giving him dirt on Biden. Then Congress impeached him again for the events of January 6, 2021.
Trump has been out of office for almost two years, and Congress is still investigating him.
That’s six presidents and three impeachments. Three and a half, if you count the Iran-contra mess. Fair odds, then, that another impeachment lies ahead.
It's not that they think he's doing such a great job, or that they don't think his scandals and miscellaneous ineptnesses don't warrant his removal, rather they surely must feasr that were he sent permanently back to his beach house in Rehoboth it would leave the country in the hands of Vice-President Kamala Harris - a frying pan/fire scenario.
It seems more likely that the Republicans will focus their fire and impeachments on folks lower down the food chain and there are lots of targets of opportunity:
As soon as Congress changes hands, Republicans will be all over Homeland Security’s response to the border crisis.The media will surely object loudly against "Republican witch hunts" and whatnot, but after four years of hounding Donald Trump based mostly on fabrications, their protestations will have little credibility.
They will deluge the White House with document requests. They will examine whether the administration colluded with social media companies to censor politically incorrect views.
They will put Attorney General Merrick Garland in the hot seat for his department’s handling of school board protests and criminalization of political differences.
And, of course, the GOP Congress will pore over the contents of Hunter Biden’s laptop.