There are plenty of metaphors to choose from when describing what newly-anointed Speaker of the House Mike Johnson is now going to have to face: a Gordian knot, threading a needle, walking a tightrope, squaring a circle, and the ever-popular herding of cats. Whatever image you choose, it all boils down to a near-impossible task -- perhaps with one very narrow solution, perhaps not. That's what Johnson now faces, with his boisterous House Republicans. The past three weeks of clown show hasn't changed the basic dynamic of this situation.

House Republicans want to pass their own individual budget bills (the 12 appropriations bills that make up the federal budget) and then they want the Democratic Senate and the Democratic president to somehow just shrug their shoulders and agree to it all. But there are a few obvious problems with fulfilling this desire, chief among them the fact that Democrats are just not going to do that, period. But let's set even that aside for the moment.

House Republicans can't even agree on what these 12 bills should say. They have managed to pass five of them (including one that passed today), but not without a lot of infighting. They say they want to pass the other seven, but none of them is have been voted on yet because the Chaos Caucus hard right is demanding uber-Draconian cuts to just about everything. These cuts are so drastic that even some Republicans are balking at them -- even though they all know that these bills will never become law. They don't even want to have to vote for such brutal budget cuts, because they know full well that Democratic challengers will use such votes in endless ads against them. And they are absolutely right about that part, it is worth mentioning.

This is the first circle that cannot be squared, but not the only one by far. Because they probably won't be able to pass all 12 bills by the middle of November, there are only two options: kick the due date down the road a bit by passing another continuing resolution to keep funding the government, or allow the federal government to shut down. Both would be problematic for Johnson for different reasons. Shutting the government down will just further prove to the American people how incapable of governing the Republican House truly is. On the other hand, passing a short-term extension of the deadline is exactly what got Kevin McCarthy booted from the speaker's chair.

Now, perhaps the Chaos Caucus folks will give Johnson a sort of "Mulligan" and allow him to pass one (and only one) continuing resolution, assumably with lots of Democratic votes and in agreement with a Democratic Senate. Perhaps they'll reason that Johnson just didn't have enough time to fix everything right away (as they see things), and they'll allow him this one compromise with the Democrats. But then again, perhaps not. Perhaps Johnson will go down in history as the shortest-tenured speaker ever. Again: this is what McCarthy got ousted for doing. And the "motion to vacate" rule is still in place.

Perhaps the House Republicans will somehow get all their budget bills done by the deadline, or (alternatively) perhaps they'll allow one Mulligan on the schedule and then pass them before the next deadline. Either way, this leads us to the biggest circle to square. Because all of those bills are going to be dead on arrival in the Senate.

This is precisely the standoff the House Republicans have wanted all along, because it will allow them to make the attempt at shifting blame for any resulting government shutdown to the Democrats, instead of them. They can say: "We passed a budget in the House... if the Senate doesn't pass our bills intact, then they are the ones responsible for shutting the government down -- we've already done our part!" This will not work, of course. Every single time the Republicans shut down the government, they have attempted to shift all the blame onto Democrats. And every single time, this effort fails -- because they public knows full well who is to blame. If history is any guide, this effort will fail once again if we reach that point.

House Republicans are going to have to compromise with Senate Democrats and the White House. That is a hard, cold fact. This is the underlying fact that is being utterly denied by the Chaos Caucus. They somehow believe they have all the leverage and will be able to just force Democrats to accept Draconian cuts (of 20-30 percent, maybe even more) to most items in the federal budget. If only their speaker backs them up and refuses to put any sort of compromise bill on the House floor, that is.

Which is the final unsquarable circle Johnson faces. If he does what the Chaos Caucus wants, the government will remain shut down indefinitely. If he strikes some sort of deal and passes a budget with Democratic votes, he will be seen as a traitor to the MAGA cause and could easily face a motion to kick him out of the speaker's chair.

The only way out of this -- the only way that needle could be threaded -- is if Johnson somehow manages to get a few select items into the compromise budget that are enough of a victory to assuage the Chaos Caucus, or at least enough for them not to fly into a rage-induced tantrum. This is highly doubtful, though. Those seven budget bills that haven't passed yet are because even their fellow Republicans balk at what the Chaos Caucus is demanding. And the Chaos Caucus won't vote for anything that doesn't have 100 percent of what they are asking for in it. Are they going to be satisfied with a few table scraps in the compromise budget? That is highly doubtful.

Republicans have gotten so insular that working with Democrats to pass bills with bipartisan support (bills that can't pass with just Republican votes) is deemed to be absolute and unforgivable treason to Republicanism. It is a mortal sin, to many of them. That is the dynamic that all these unsquarable circles spring from. And that is what Mike Johnson now faces. In three weeks' time, he will be at his first juncture in this conundrum. Perhaps he worked out a Mulligan with his conference before becoming speaker, and perhaps he'll be allowed to pass one short-term continuing resolution to keep the government open. But even if that is true, he's only going to be allowed to do this once before facing exactly what Kevin McCarthy faced: on the one hand, the reality of having to compromise with Democrats; on the other hand, the fact that a faction of his own Republicans do not accept this reality. And they're quite willing to punish any of their leaders who do.

-- Chris Weigant

Follow Chris on Twitter: @ChrisWeigant