Speaker Boehner, Incoming Leader McConnell, get on this right away.
Do it for this sole reason: The impeachment resolution will get through the House, it will go precisely nowhere when tried in the Senate, and the Republicans will look like bigger idiots than they already do.
Constitution, Article 1, Section 3, Clause 6:
"The Senate shall have the sole Power to try all Impeachments. When sitting for that Purpose, they shall be on Oath or Affirmation. When the President of the United States is tried, the Chief Justice shall preside: And no Person shall be convicted without the Concurrence of two thirds of the Members present."
54 Republicans in the Senate does not 2/3 make. There are not 13 Democrats who would go along with them on removing the President. (Honestly, the 2014 election purged many red-state Dems who otherwise might have had the slightest of temptations.)
Oh, and Chief Justice Roberts, the G.W. Bush-appointed "savior of Obamacare" would preside over the doomed trial.
So, Speaker Boehner, please proceed. The Constitution grants the impeachment power to the House, so you have to man up and make good on your threat. Most of your base probably thinks "impeach" means "kick out", having failed to read the Constitution they claim the President is trampling upon. Deal with their backlash when they realize that you certainly did impeach him, but he is still in office. Give them their red meat, and let them see that it was pink slime all along.
Please, Mr. Boehner, waste more of Congress' time on frivolous things, we need you to look as clownish as possible in 2 years time.