An impeachment of Bush and/or Cheney for an indisputable offense (refusing subpoenas, refusing to enforce contempt citations, rewriting laws with signing statements, openly violating the Foreign Intelligence Surveillance Act, etc.) could take literally one day. Such a thing would not be unprecedented. President Andrew Johnson was impeached three days after the offense for which he was impeached. Senator William Blount was impeached four days after the offense for which he was impeached.
There is no reason impeachment hearings on Cheney or Bush should be limited to the simplest crimes or rushed through at top speed. Public education might benefit from a slower process. My point is only that it is possible to impeach rapidly. A senate trial can also serve as an educational forum. Below are some of the dates I've been able to find on how long past impeachments have taken. A better researcher might add to this collection. In several cases, I have dates for the duration of the Senate trial, but not for the House impeachment, the duration of which may in fact have been negligible.
A Senate trial can also be completed quickly, and there is no requirement or precedent for including every obvious impeachable offense. (In fact, there is no precedent for elected officials being guilty of so many obvious impeachable offenses or for the public being so aware of impeachable offenses prior to an impeachment.) The Senate expelled Blount the day after he was impeached. Judge Halsted Ritter's Senate trial took 11 days. Judge John Pickering's trial took nine days. Judge James Peck's trial took three days. Judge West Humphreys' trial took one day.
Johnson was impeached three days after committing the offense for which he was impeached, and prior to drafting articles of impeachment. Within a week, a committee drew up charges, and 11 days after the offense, the House delivered the charges to the Senate. The trial process began the next day, and in under three months it was over.
The House began impeachment procedures for Bill Clinton on October 8, 1998, and impeached him on December 19th. The Senate trial lasted from January 14, 1999, to February 12, 1999. The whole four-month farce took less than half the time remaining to Bush and Cheney.
Most impeachments have not been against presidents, but rather judges, cabinet officers, senators. These impeachments seem to take about as long as presidential impeachment do, and offer no support to the myth of long impeachments. In addition, much other business has been accomplished at the same time as these impeachments.
On July 3, 1797, evidence of an offense by Senator William Blount became known. Four days later, the House impeached him and the next day the Senate expelled him.
Evidence of an offense by Judge John Pickering became known on February 4, 1803, and the House voted to impeach him on March 2, 1803. The Senate didn't try him for another year, but spent 9 days on it when it did so.
Supreme Court justice Samuel Chase was impeached in late 1804 (I don't know how long the impeachment took) and 30 days later he was tried in the Senate, which completed the trial on March 1, 1805.
Judge James Peck was impeached on April 24, 1830, a month after the Judiciary Committee recommended it. The Senate took up the trial the following January and spent three days on it.
Secretary of War William W. Belknap was impeached on March 2, 1876, and the Senate trial was completed on August 1, 1876.
Judge Charles Swayne was impeached on December 14, 1904, and his trial was over on February 27, 1905.