Will the US default soon?

Quite possibly.
We have a toxic mixture of overspending, insufficient revenue to cover the spending, and a borrowing limit. Several ideas have been floated over the last few weeks, including minting a $1T USD coin and depositing in the federal reserve. Thats $1012 USD folks. This is sort of like quantitative easing, aka printing more money, but far far worse. Anyone whom has ever been early into a startup and watched the value of their options get diluted with each new capital infusion knows exactly what this is. But the scale of this is so huge … it would massively devalue existing currency, and we’d be begging for Zimbabwean level hyperinflation as a relief to what we’ve done.
As zerohedge notes, this would be positively Weimerian. A useful quote (ignore that it is Keynes saying it, even broken clocks are right twice a day) from the article is

John Maynard Keynes described the situation in The Economic Consequences of the Peace: “The inflationism of the currency systems of Europe has proceeded to extraordinary lengths. The various belligerent Governments, unable, or too timid or too short-sighted to secure from loans or taxes the resources they required, have printed notes for the balance.”

which, if you go look up Quantitative Easing, you find this

Quantitative easing (QE) is an unconventional monetary policy used by central banks to stimulate the national economy when conventional monetary policy has become ineffective.[1][2] A central bank implements quantitative easing by buying financial assets from commercial banks and other private institutions, thus creating money and injecting a pre-determined quantity of money into the economy.

That is, the hyperinflation was the result of effectively waving a magic wand, and printing the money … creating it from whole cloth, or solid metal … the mechanism matters not at all.
This is not the train we want to ride. Really.
So our choice is to borrow more, cut our spending, or become the Weimar republic or Zimbabwe.
Seems like we should cut our spending. Just let the sequester hit. Doesn’t matter where. Let it take hold.
Give a small, temporary bump, with a sunset clause, to the borrowing limit. So that we can be over that limit for a small interval. 30 days, 60 at most. Then use the savings from the spending cuts (which have to be much larger than the bump up) to start paying down the balances. Even better, put this on a time table in the bill, so not only is the bump sunsetted, but even better, every 60 to 90 days, new cuts must be made, with the savings used to pay down the existing debt.
This is what a family with maxed out credit cards would do. This is what a business with maxed out credit facilities would do. See the pattern? We have to do this as a country.
There are costs to bad decisions. Very real costs.