All this last-minute haggling, coupled with the Senate's more sedate legislative pace, means both chambers may need to pass a continuing resolution covering a couple of days before a final bill can make it through and shut the lights on the crummiest and least productive Congress of the modern era.
While there will be some drama, the risk of a shutdown is fairly low because leadership in both parties wants to avoid it and the power of the tea party caucus is probably not enough to overcome larger desires on both sides to go home for Christmas and forget the 113th session ever happened.
Read MoreRomney run won't depend on Jeb: Ben White
Republicans, freshly in charge of both chambers, want to open 2015 with a mostly clean slate other than the next fight over funding the Department of Homeland Security, which won't be in the so-called "CRomnibus" set to pass this week so Republicans can say they fought Obama over his unilateral immigration actions. (CRomnibus is a fittingly Frankensteinian conflation of "Continuing Resolution" and "Omnibus" spending bill.)
But that won't be a real fight next year because there is no way the GOP is going to begin the pre-presidential year Congress by denying funding to an agency that monitors the border and otherwise defends the nation. GOP leadership is trying to do just enough in the year-end spending bill to give more conservative members a talking point to say they fought Obama over immigration without actually incurring any collateral political damage by shuttering the government in the height of the holiday season.
The skirmishing now is mostly over how much the GOP can cram in the bill without losing the bloc of Democrats they will need to get the bill through the House. There is always a chance that these skirmishes will lead to total collapse and a brief shutdown. But it's a small chance. So far, the White House is not warning of a veto of a CRomnibus that excludes Homeland Security, and House Minority Leader Nancy Pelosi is not encouraging members to vote against the bill.
So the odds favor a House vote by Wednesday and final Senate passage by late Thursday. That could slip into Friday or even the weekend with a short-term CR, but there's almost no chance the government fails to open for business on Monday.
Read MorePresident Barack Obama Appears on 'The Colbert Report'
This will still leave a number of important items hanging over into the next Congress before the new GOP majorities can try to move on whatever their new agenda turns out to be. There will likely be fights over Obama's nominees for attorney general and defense secretary, but both should ultimately be confirmed. There will also be a heavy debate over an Authorization for the Use of Military Force (AUMF) covering the current fight against ISIS. And Obama may have trouble persuading liberal Democrats to support his nomination of Lazard banker Antonio Weiss to serve as undersecretary of Treasury for domestic finance.
All of this will lead up to debate over raising the debt limit, which will happen sometime in late spring or summer. That could get dicey if Republicans demand big concessions on spending, Obamacare or anything else. But the dynamic will be completely changed with the GOP as the dominant governing party in Congress with the responsibility not to default or even threaten to do so.
Read MoreHolder Unveils Revisions to Limits on Profiling by Federal Law Enforcement
In any event, the debt limit is a discussion for another day. Right now, the 113th Congress is likely to have one last dysfunctional squabble over funding the government for old times' sake before receding into the history books.
—By Ben White. White is Politico's chief economic correspondent and a CNBC contributor. He also authors the daily tip sheet Politico Morning Money [politico.com/morningmoney]. Follow him on Twitter @morningmoneyben.