No Legal Framework
The US government hasn't intentionally defaulted since FDR's presidency. Even then, that was a planned default, which is not what the Tea Partyers want. They want prioritized payments of US obligations to avoid default and do the least harm to the country.
No such prioritization has been established, so this is new territory. There aren't laws laying out how to do this. In the absence of such laws, who will decide what the priority should be? That's a huge constitutional question. Does the president unilaterally decide since he's the executive? Does the Congress decide? Can Congress impeach the president for making unilateral decisions? Can Congress impeach the president for refusing to prioritize payments? Will the Tea Partyers who want the prioritization of payments guarantee that they won't call for Obama's impeachment over the decisions he makes in this regard? I sure haven't heard anyone making such a promise.
Will Congress quickly pass the legal framework required? HAHAHAHAHA.
No Practical Mechanism
All the accounting programs, sign-offs, clearances, etc. that it takes for the government to send money to the correct people are probably much more complex than anyone's monthly disbursements. How readily can that all be changed to send out prioritized payments? Not readily, I'd bet. There would need to be an entire design/implementation cycle with the requisite planning, programming, testing, bug-fixing, and retesting.
Political Motivation (1)
So those who support prioritized payments will probably also want a big say in determining the priorities. But again, there is no legal framework at this time for that. Congress would need to follow the usual law-making procedures--but the chance that the House, Senate, and president will pass one prioritization plan is so close to zero, it is effectively zero. So there will be no prioritization in established law.
I've never heard any proponent of prioritization discuss this wrinkle in their plan. I'm guessing that they gloss over that impediment, and imagine that their priorities are so obvious that they'll be followed. Then, reaching the debt ceiling is equivalent to immediately going to a balanced budget. By refusing to raise the debt ceiling, they achieve one of their biggest policy goals. And they didn't even have to pass a balanced budget law or amendment. Hooray! No wonder they gloss over so many details.
So if priorities could be established, Tea Partyers have another way to achieve a major goal--just don't ever increase the debt ceiling. That's a lot of added leverage for them in any budget negotiation.
Political Motivation (2)
What is the political motivation of the Democrats, including the president? They aren't for an immediate balancing of the budget. They aren't for establishing spending priorities at a much lower budget target point. They don't want the Tea Party to have greater leverage in budget talks. Their motivation is to make the debt ceiling as painful as possible, so that the GOP will always back down.
In this, they have history on their side because the debt ceiling has always been increased. Neither Congress nor the president has ever stepped over that line, because it would be too catastrophic a move to make. The US government would go into default, which would destabilize the world economy and probably cause a worldwide depression.
The Democrats have no reason to make the debt ceiling less scary. That hands leverage to those who want severe budget cuts, which are not the Dems. So there's no way that the Dems will pass any legislation that prioritizes payments in the event of reaching the debt ceiling.
Maybe the next time the GOP controls the House, Senate, and presidency, they can pass the legislation and build the accounting mechanisms to implement prioritized payments. That will be somewhere on their list of must-have legislation including the repeal of Obamacare, rolling back regulation, closing the EPA, block-granting Medicaid or just getting rid of it, outlawing abortion, and ushering in the permanent GOP majority.
Maybe, like Rip Van Winkle, I'll go to sleep for two decades, and then wake up to a US where all this has happened. Somehow, I doubt it, but we'll see. Nighty-night!
Come on, it's simple.