Updated at 1:55 p.m. ET

In an emotional return to the Senate floor on Tuesday afternoon, Sen. John McCain admonished the leaders of his party for how they managed the health care bill and called instead for "regular order."

"Let's trust each other. Let's return to regular order," the Arizona Republican said. "We've been spinning our wheels on too many important issues because we keep trying to find a way to win without help from across the aisle."

That rather vague-sounding phrase — "regular order" — actually has a more concrete meaning, and it is highly relevant to the situation the Senate finds itself in right now.

After months of struggling to make good on their vow to repeal and replace the Affordable Care Act, also known as Obamacare, Senate GOP leaders are still without a plan that has the support of 50 members. That may have been the fruit of a process by which GOP leaders bypassed the usual steps of public hearings and committee deliberation, relying instead on a "task force" that met privately to produce a bill.

On Tuesday, the Senate did vote to bring the health care debate to the floor. That vote opened up hours of debate and amendments that have so far failed to garner enough Senate support to pass. Much of what is being debated and voted on now emerged from the leadership itself this spring and summer, the products of a secret task force organized as an alternative to — wait for it — regular order.

"Regular order" refers to the procedures and processes that have governed the Senate for generations. It consists of rules and precedents that have been followed with few exceptions for legislation both big and small.

But regular order is not only a process, it is also a state of mind. It implies not only procedures but also a presumption of at least some degree of bipartisanship.

The supermajorities that are required in the Senate — notably the 60-vote minimum to end a filibuster and close debate — have meant leaders of both parties had to look for support across the aisle and to make accommodations.

That is the tradition that has been lost in recent years, as whichever party has the majority gets frustrated by the minority party's power to jam the works. Pressured by presidents and the media, the majority leadership has done what it could to circumvent regular order.

"That's an approach that's been employed by both sides," McCain noted in his floor speech Tuesday, "mandating legislation from the top down without any support from the other side, with all the parliamentary maneuvers that requires."

Regular order might also be called "doing things the old-fashioned way." The way you heard about Congress in school. A bill is proposed to the body. Leadership assigns it to a committee, or more than one. Then the chairman of the committee decides whether to consider it and when. Public hearings are scheduled in coordination with the ranking (most senior) member of the opposition party on that committee.

After the hearings, the chairman brings forward a version of the bill he or she likes and schedules a "markup" to consider amendments. The members of the committee from both parties offer amendments, debate them and vote on them.

If the committee likes the amended bill enough to approve it, the next step is floor consideration. The gateway to the floor is a "motion to proceed," which, in recent times, has often been filibustered.

To beat the filibuster, leaders in both parties have fallen back on the budget reconciliation process, which cannot be filibustered. Reconciliation was intended for strictly fiscal measures that kept the government operating, but it has been used more creatively to pass measures that stretch the original boundaries.

That was the case for the Democrats desperate to pass budget additions to Obamacare in 2010, and it's the case now for Republicans desperate to repeal it.

Such use of reconciliation can defeat the filibuster tactic but at the price of destroying the last vestiges of bipartisanship. And the consensus-building that was once the hallmark of the Senate. Just ask John McCain.

If the Senate was to return to regular order, in theory, the last step of the process would be a floor vote to be decided by a majority. Then if the House has passed its own version of the bill, there's a conference between House and Senate to make sure their versions are the same.

Then it goes to the president for the signature that enacts it into law.

That's regular order. In practical terms, regular order is slow and tends to get bogged down. In practical terms, it may mean processing an idea to death or talking a bill to death.

That was why, when it came to repealing Obamacare, Senate Majority Leader Mitch McConnell decided to short-circuit the process and have a special task force instead. And that task force produced a bill, which McConnell and the other leaders have massaged and fixed up and tried to get a majority of the Senate to accept.

When they couldn't manage to get to even 50 votes, several senators began calling for regular order. McCain was one: He said it was time to go back to regular order and have public hearings and committee process.

And that is one possible outcome of the latest frustration in the Senate.

Or we might just go back to another task force and another round of tweaks by the leadership. That would be a lot faster. But it might not produce a bill that a majority of the Senate can vote for.

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