This article is from the archive of our partner National Journal

It may be hard to believe, given the stumbles of the last three months, but the new Republican majority on Capitol Hill is about to face its biggest challenge yet.

After running on a platform of fiscal responsibility, Republicans in the House and Senate are set to release their budgets on Tuesday, showing the American public their blueprint for putting the country on a more sustainable fiscal pathway.

After ceaselessly mocking Senate Democrats for not being able to pass a budget over six years during their majority, Republicans will have their own shot to get a budget resolution through both chambers. And for the first time this year, leaders will only need their own members in order to pass the resolution.

But it's unclear whether House Speaker John Boehner and Senate Majority Leader Mitch McConnell can actually get there. With conservative distrust in Boehner growing and McConnell only able to lose three of his members to maintain a majority, both leaders will have to thread an incredibly small needle to pass a budget in their own chambers, much less both of them.

(RELATED: Boehner's New Strategy: Enlist Democrats First, Not Last)

The GOP effort could fall apart in any number of ways. Here are three of the most dangerous minefields facing the leaders.

DEFENSE SPENDING. The biggest problem facing Republicans is the divide between fiscal conservatives and defense hawks.

This is a particularly difficult issue in the Senate, where hawkish Republicans—including Sens. Tom Cotton, Lindsey Graham, and John McCain—have already said that they cannot support a 2016 budget that leaves in place the Budget Control Act caps on defense spending. If any other member were to join them—including fellow hawks such as Sens. Kelly Ayotte, Mark Kirk, and Roger Wicker—there goes the budget. Game over.

Members of the House Armed Services Committee and appropriators in the lower chamber also have threatened to jump ship over the defense caps, making it even more difficult for Boehner to strike a balance with his own members. House leaders have been trying for weeks to solve this puzzle.

But if budget-writers concede to hawks' demands and raise the caps on defense spending, they're likely to run into an all-out revolt from conservative members. When Congress altered the spending caps in the Ryan-Murray budget deal last year, 62 House Republicans voted against the bill. Boehner can only afford to lose 27.

(RELATED: House GOP Wants to Give Pentagon a Boost)

Conservative groups such as Americans for Tax Reform, Americans for Prosperity, and Taxpayers for Common Sense have pushed hard to maintain the caps, arguing that defense spending in 2016 under sequestration will actually be about $2.2 billion higher than it was in 2015. "Fiscal discipline is needed across the federal government, and that includes defense spending," several groups wrote in a letter to House Budget Chairman Tom Price earlier this year.

Both the House and Senate budgets are expected to maintain the overall sequestration caps. Senate Budget Chairman Michael Enzi has said the Budget Control Act is the law of the land and the budget should reflect that.

But that hasn't satisfied hawks in either chamber. In a concession to defense-minded members, Price has raised the possibility of raising the defense caps and lowering those for nondefense spending to maintain the overall funding levels. And in the Senate, Graham and McCain are working with Democrats on an alternative that would set up a reserve fund in the budget resolution to increase funding for defense.

Still, the budget resolution can only suggest changes to sequestration. If members want to alter the actual spending caps, they'll have to pass a law to do so, and that will require 60 votes in the Senate.

2016. The 2016 campaign provides Senate Republicans with further divergence in their ranks—and more possible headaches. Twenty-four Republicans are up for reelection, with about eight vulnerable members in blue and purple states. Those members, including Ayotte and Kirk as well as Sens. Ron Johnson and Patrick Toomey, will be wildcards in the budget process, potentially unwilling to go too far to the right.

Making matters even more difficult, the budget resolution isn't actually law. It's merely a blueprint for appropriators to work off of as they design their bills to fund the government later this year. That will happen whether or not the Senate passes a budget. Particularly if the House seems unwilling to play ball with their colleagues in the upper chamber, vulnerable Republican members may well decide that it's less risky to shoot down a conservative budget blueprint than to take a tough vote on something that won't ever be signed by President Obama.

(RELATED: How Republicans Could Blow the Budget)

But in appealing to the more moderate and vulnerable members of his party, McConnell stands to lose the votes of some of his members who are considering running for president in two years. Eager to differentiate themselves from a crowded Republican field and to appeal to primary voters, who tend to be more conservative, Sens. Ted Cruz, Marco Rubio, and Rand Paul are likely to want to stake out conservative territory during the budget fight.

RECONCILIATION. Assuming the House and Senate agree on a budget resolution, and that's a big if (see above), they'll still have to make a decision about reconciliation. The powerful procedural measure would allow members to make major changes to current law with a simple majority vote in both chambers.

Republican leaders have been telling their members, particularly conservatives, for months to focus on reconciliation as the big prize at the end of a budget deal, but that it needs to be moderated to pass both chambers.

Although leaders have kept their cards close to their chests on how they'll use reconciliation, Republicans have spent the last several months discussing their options, including overturning the Affordable Care Act and using the move to defund Obama's executive actions on immigration.

The problem: Conservatives know that reconciliation is an empty promise. With Obama still in the White House, he will almost certainly veto anything Republicans send him via reconciliation. Members are "overly optimistic about what all can be accomplished" through reconciliation, Taxpayers for Common Sense Vice President Steve Ellis said Monday. "Anything that you could get that you would actually expect to get signed into law, you could have probably just gotten normally."

It is possible that Republicans could earn enough votes from Senate Democrats wary with Obama's actions on immigration to overturn or defund them, but that's a big if. Whether conservatives are willing to take that gamble remains to be seen.

This article is from the archive of our partner National Journal.

We want to hear what you think about this article. Submit a letter to the editor or write to letters@theatlantic.com.