The next 48 hours promise to be among the most politically pitched in recent years with a Republican House and a Democratic Senate trying to pass a 2011 budget and, in so doing, avoid a government shutdown.

Even though a slim majority of Republicans now say a shutdown is an acceptable outcome, even GOP leaders recognize the political peril involved in letting funding of the government lapse.

But the prospect of a shutdown is only growing, with Senate Majority Leader Harry Reid (D-Nev.) saying Thursday morning that Congress “is heading in that direction.”

It’s anybody’s guess whether that will actually occur but the debate over the next 36 hours could set the tone for the next two years of relations between Congress and the White House.

As you watch the drama unfold, we thought it worthwhile to point out some of the key players, pivotal figures and members whose support could highlight a larger shift in the debate.

* Sen. Rand Paul (R-Ky.): No member of Congress more embodies the tea party rise and spirit than the freshman senator from Kentucky. And with tea partiers the most supportive of a potential government shutdown, Republican leaders will have to take their cues from what Paul says in the coming days. Interestingly, Paul is not among the tea party crowd actively suggesting a shutdown. In fact, he said in November that it would be a mistake to force a government shutdown in order for the GOP to get the cuts it wants. But he’s also been pretty quiet in recent days and was evasive when asked whether he would support a bill that cuts less than the $500 billion in his own proposal. He’s not getting $500 billion in cuts – or anywhere near it – so he will be forced to take a position sometime soon.

(Adding to the drama is the emerging talk that Paul may run for president in 2012. The potential government shutdown – not to mention an actual government shutdown – gives a member like Paul a platform in the coming days that no other tea partier will have. How does he handle it? Does he start speaking out more? Does it become a launching pad for a presidential bid? Does he try to steer the tea party in one direction or another?)

* Republican Study Committee Chairman Jim Jordan (R-Ohio): Jordan leads a group that includes the most fiscally conservative House Republicans. That means Jordan has the juice to sway dozens of Republican votes. If there is to be a compromise, Jordan could play a key role in facilitating it and selling it to more conservative members. He will also reportedly support a one-week continuing resolution, which would fund the government through next week, after voting against the last one. That’s important, because the number of Republicans resisting the continuing resolution grew substantially between the first and the second versions. That said, Democrats have said the third continuing resolution is a non-starter because it cuts too deep and in the wrong areas.

* House Minority Whip Steny Hoyer (D-Md.): Besides being the former House majority leader, Hoyer is that guy that can bring moderate House Democrats on board and the person Republicans think they can work with best. That said, he and current Majority Leader Eric Cantor (R-Va.) had a very spirited debate on the House floor around the noon Thursday — complete with repeated outbursts from the assembled members of Congress and plenty of frustration over the current standstill. If Jordan is the guy who can deliver votes from the right, Hoyer is the guy who can deliver votes from the left-center. If he’s standing firm, the moderate-to-conservative wing of the Democratic caucus is likely to be doing the same.

* House Speaker John Boehner (R-Ohio): Nobody in Congress faces more political peril right now than the new House speaker. It was always going to be a balancing act for Boehner between the tea party and the more traditional Republicans who were already in Congress, and we’re seeing that situation come to a head in a major way for the first time. Republicans won big in 2010 largely because of the energy of the tea party. Now that same tea party is expecting its new Republican House majority to govern with tea party values. Boehner is doing his best to assuage both sides — saying there is “no daylight” between him and the tea party but also emphasizing that a shutdown isn’t the answer. But when the rubber meets the road, he may very well have to choose between satisfying his base and keeping the government running. It’s not an enviable position.

* White House Chief of Staff Bill Daley : Since taking over as President Obama’s new chief of staff, Daley has been seen as a moderating force, moving the President to the middle on the key issues of the day. That is especially true on spending issues. If it comes down to the final hours and the White House is working hard to avert a shutdown, it’s not hard to see Daley being the guy in the room who is willing to compromise a little more than the others. He’s been central in negotiations, reportedly coming to an agreement with Boehner’s staff on $33 billion in cuts last week, but Republicans say no agreement was ever in place. All negotiating aside, Daley has basically dared Republicans to force a shutdown. Like Hoyer, Daley can be a GOP asset or a deal-breaker.

Paul Kane contributed to this post.