It’s a bit more urgent than that: The GOP knows they’re about to lose their majority in the house so this is the only chance they’ll get to do something like an impeachment. If they put it off any longer they’ll run out of time while the investigation committee follows a normal (intentionally slowed by opposition) congressional schedule. They know that the whole exercise will be pointless if they can’t get it done now because doing it any later will result in the investigation committee having nothing to report in time for the next election.
More importantly: They have no other ideas. They literally have no other bills or even inklings of an idea as to how to grab America’s attention in anything resembling a positive or even neutral light. They lost abortion as a wedge issue now that Roe V Wade was overturned so the GOP is basically out of ideas because while they love to hate immigrants and LGBTQ people they don’t have any politically useful legislation to bring up before the next election. Nothing they can pass to say, “see? We did something and the Democrats in the Senate blocked it!”