(CNN) -- We all know the Schoolhouse Rock song about how a bill becomes a law. You know, "I'm just a bill, yes, I'm only a bill, and I'm sitting here on Capitol Hill"? If Senate Majority Leader Harry Reid and his Republican counterpart, Mitch McConnell, can come up with a deal Tuesday to end this governmental gridlock, a number of things will have to happen in fast forward to beat the Thursday deadline to lift the debt ceiling.
1. The Senate has to pass a bill -- quickly
Conservatives might oppose it -- and another filibuster-type stall tactic could drag the process on for days. Sixty ayes are needed to end floor debate.
2. The House has to pass the same bill
No matter what the Senate agrees to, the House also must agree for this to get to the finish line. It's not at all clear that conservatives in the House will sign onto a proposal they dislike.
Some still want to pass a bill with major changes to Obamacare, not merely the minor ones reportedly included in the Senate plan under discussion, and many are committed to spending reforms and are looking for a long-term deal to lock in those changes.
"One thing we don't want to see is another patch where in a couple weeks later we're in the same spot again," Rep. Steve Scalise, R-Louisiana, said Tuesday on CNN's "New Day."
"The President will have to agree to sit at the table and start negotiating on the long-term issues," he said. "We've been saying this for two weeks. We're ready to do it."
It's possible that a compromise bill could pass with a coalition of moderate Republicans and the House's Democratic minority, which has happened before on compromise deals on the so-called "fiscal cliff" tax increases and spending cuts and emergency aid to Superstorm Sandy victims.
But House Speaker John Boehner would have to allow a vote first. He's under intense pressure from the right not to make concessions to Democrats. And while he has said he will not allow the nation to default on its debts, it's less clear he would sidestep his party's more conservative wing to bring a shutdown-ending deal to a floor vote.
Finally, if we do have a vote, we could see the House and Senate batting amendments back and forth, much as they did before the shutdown, and that could push approval of the legislation past the debt ceiling deadline.
3. The President has to sign it
Once the chambers sign off, whenever that might happen, there's still that other question: Will President Obama accept the concessions made by both sides? Yeah, they didn't teach you this verse in the "'I'm just a bill" song.
Obama has signaled that he is willing to accept a short-term debt-ceiling deal and to negotiate on issues important to Republicans, but not without an agreement to reopen the government.
But before it gets to that, Tuesday will bring:
Meetings of the players
As if there have not been enough meetings or rumors of meetings or postponed meetings, Tuesday will start off with, you guessed it: more meetings. House parties will meet first, followed by lunch meetings by Senate parties. A good clue on early progress will come first from House Republicans. They should be the first to get in front of cameras.
Obama on the television
The President is expected to pop up on several local TV stations Tuesday, no doubt with markets in key congressional districts. Also, there's a midday White House media briefing that may give hints on how Obama feels about developments. If both parties get close to a deal, expect the White House to give definitive word on whether or not the President would sign off on it.
Markets on the watch
Whatever happens Tuesday, expect the markets to react. Economists say the closer we get to the debt ceiling deadline, the more this uncertainty can affect the markets. Early reports indicate that the Asian markets are responding positively to the news of progress. But domestic banks are reportedly coming up with contingency plans in case Congress goes past the deadline. Any news Tuesday is bound to change things.
CNN's Steve Almasy contributed to this report.