As the House returns Monday, Speaker John A. Boehner faces two big tests of his hold on the ever-unruly Republican Conference: pushing through the GOP budget and putting the final touches on a speaker-approved Medicare “doc fix.”

After days of closed-door whip checks and haggling on amendments, the House Budget Committee advanced its fiscal 2016 budget on March 19 by a 22-13 vote. Every Republican supported the measure in committee, but GOP leaders are unlikely to be so lucky if the bill comes to the floor next week, as leaders said it would.

The Budget Committee did not vote, as defense hawks had wanted, on an amendment adding more money to an Overseas Contingency Operations fund. House Armed Services Committee Republicans have threatened to withhold their support for the budget if they don’t get additional dollars for the Pentagon, and if the 36 Republicans on the committee band together to vote against the budget, the measure would almost certainly fail. No Democrat is expected to vote for the GOP blueprint.

Budget Chairman Tom Price, R-Ga., told leadership an amendment adding OCO money simply couldn’t pass his committee, but leaders didn’t believe him. After going around Price and doing their own whip count, they insisted Price add the money to appease the defense hawks.

Only leadership had the count wrong — at least on an amendment that didn’t offset the extra $2 billion. There weren’t enough votes to add anything more to defense without taking from other accounts. Eventually, the Budget Committee advanced its bill without the amendment.

But not all hope is lost for the defense hawks. Speaker John A. Boehner suggested the Rules Committee will add the $2 billion, avoiding a messy floor vote on such an amendment.

That approach comes with its own problems: If GOP leaders appease defense hawks, even if it’s just $2 billion, they’re sure to upset the fiscal hawks who already think the budget is gimmicky and doesn’t cut enough.

According to House Republicans, the budget achieves balance by 2024. It does so, however, by repealing Obamacare, something no Congress is likely to do any time soon. And in their 10-year projection, Republicans account for roughly $2 trillion of the $5.5 trillion overall in cost-cutting by trashing the health care law. Most of the rest of the savings — more than $2 trillion — would come from reducing growth costs associated with Medicare, Medicaid and the Supplemental Nutrition Assistance Program. That’s unlikely to happen.

Conservatives can find plenty to disagree with in the budget, it’s just a matter of whether they will. Right-leaning Republicans suggested they might be more open to the blueprint because it could set up a conference with the Senate — assuming the Senate is able to pass its own budget — and all the two chambers to use reconciliation to tackle a number of legislative items, such as Obamacare.

That prospect — another sort of wishful thinking — might make passage a little easier. Either way, the GOP budget is unlikely to just sail through the House. It will take arm-twisting and a precise, disciplined vote count, something the GOP leadership has had trouble with recently.

The House is loosely slated to vote on the budget Wednesday. (It’s also worth watching the Republican Study Committee budget vote, when Democrats typically vote present in order to make Republicans vote down an even more conservative budget proposal.)

All the budget fun and games will leave little time, perhaps by design, for the House to take up legislation eliminating the sustainable growth rate.

The “doc fix” proposal has been championed by the speaker as a long-overdue first step to reining entitlement costs.

A deal to come up with a more reliable Medicare payment formula for doctors had seemed in question for quite a while on Capitol Hill. But every day an agreement doesn’t blow up is a day closer to a deal.

While the specifics haven’t been released, it looks like Congress is aiming to ditch the SGR and pay for it — some of it, at least — by making wealthier seniors pay more for Medicare and by imposing small deductibles on Medigap plans. Those aren’t the most ambitious changes in a potential “entitlement reform,” as Boehner and his allies are calling it, but the proposal does set a precedent of Democrats not getting tax raises with any changes to Medicare or Social Security.

While some conservatives might not like the idea of giving up the yearly opportunity to extract spending concessions, other members are bubbly about the potential future savings and the prospect of tackling Medicare — even if it is on the margins and even if these are changes that President Barack Obama himself suggested.

Many Republicans argue Congress wasn’t really paying for SGR patches anyway, so any dollar they get in savings is a dollar they wouldn’t have had. At this point, it doesn’t seem like conservatives are the greatest threat to a deal; it’s Democrats.

Boehner has always seemed likely to rely heavily on Democratic votes to pass a long-term bill. But Senate Democrats, catching wind of what’s going on in the House, look like they’re pushing for a sweeter deal. According to a source familiar with the Nevada Democrat’s view, Senate Minority Leader Harry Reid thinks the SGR agreement “stinks.”

This may all be theater — either to try for more concessions or to make conservatives think they’re getting a better deal than they are — but if Democrats balk at the SGR deal, Boehner might not have many options.

Sources familiar with the negotiations tell CQ Roll Call Democrats are getting two years of the Children’s Health Insurance Program included in the deal, but it seems like Senate Democrats believe they could get four years. Much of this late opposition to the House deal could be to help Democrats get better terms on those sorts of items.

Either way, Congress needs to come up with something before March 31, when the current SGR patch expires and Medicare payments to doctors would be reduced 21 percent.

Before the House gets to the big-ticket items of the budget and SGR, it’s set to first vote on six suspension bills, including a measure allowing an income review every three-years for families receiving certain federal housing programs and a bill reauthorizing a housing assistance program for Native Americans.

Paul M. Krawzak contributed to this report.

Related:

Fiscal Conservatives Buck Leadership, Send Tighter Budget to Floor (Updated)

Quiet Win for Boehner? Bending the Entitlement Curve

Republicans Open to Potential ‘Doc Fix’ Deal

The 114th: CQ Roll Call’s Guide to the New Congress

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