An agreement on the United States’ debt ceiling doesn’t necessarily mean a smooth path to President Joe Biden’s desk. The president and House Speaker Kevin McCarthy reached a final deal Sunday on raising the nation’s borrowing limit that, if passed by Congress, would avoid a default on U.S. debt . Next comes the political wrangling, which means it could still be a tense week. The House is expected to vote on the Fiscal Responsibility Act on Wednesday. Then, the Senate will take it up, with all eyes on Monday, the so-called X-date the Department of the Treasury said is the earliest the government could default. “The deal will face some headwinds as it winds its way through both chambers of Congress, and we should be prepared for headline volatility as these types of packages die a dozen deaths right before passage, but we remain committed to our view that a package will clear before we hit the nation’s debt ceiling on June 5,” BTIG director of policy research Isaac Boltansky wrote in a note Monday. Several Wall Street economists agree the deal will likely get signed, but not without some bumps along the way. Still, Tobin Marcus, Evercore ISI senior U.S. policy and politics strategist, doesn’t expect an outsize market reaction on the bill’s way to the finish line. “We cannot yet entirely rule out the possibility of a blow-up, but … we expect this bill to make it through Congress this week and be signed into law before the X Date,” he wrote in a note Tuesday. “Given how this is priced in, we do not expect significant market reactions to Congressional milestones barring a TARP-style disaster.” Here are some of those potential headwinds the legislation may face in the coming week. Congressional Budget Office score Boltansky is concerned the Congressional Budget Office score on the package could show the deficit reduction is modest in relation to the United States’ fiscal position, but he doubts it would derail the deal. The CBO, a nonpartisan federal agency, provides objective budget and economic data to Congress. “There is always wide latitude in how those figures are framed (e.g. out-year assumptions, etc.),” he said. “For example, a preliminary CBO report estimates that the debt ceiling package could reduce spending by $2.1T if the proposed budget caps are left in place for a full six years, which is possible but unlikely given the mechanics of the legislation.” House Committee on Rules meeting Before the legislation reaches the House for a vote, it must go through the 13-member House Committee on Rules — nine Republicans and four Democrats. However, despite the GOP majority, the meeting Tuesday afternoon could be “messy,” Boltansky said. “There could be some headline volatility Tuesday afternoon,” he wrote. Goldman Sachs chief economist Jan Hatzius also sees the committee meeting as a point of uncertainty, although he expects the ultimate passage of the deal is very likely. Two Republicans, Reps. Chip Roy and Ralph Norman, appear to oppose the bill, and the position of a third, Rep. Thomas Massie, is unclear. “If all three vote against and no Democrat votes in favor, the bill will fail,” Hatzius wrote in a Monday note. “That said, we think the Rules Committee is very likely to send the bill on to the House Floor, as we think a majority of the committee will vote for the package even if it takes Democratic support (it is uncommon but not unheard-of for the minority party to support the majority party’s efforts in the Rules Committee).” Evercore’s Marcus agreed. “This will be interesting as a lens into the internal politics of the House GOP, but even if Massie decides to vote against the bill, we would be very surprised to see the Dems on the Rules Committee kill a deal struck by Biden,” he said. McCarthy no confidence vote Meanwhile, Michael Gapen, Bank of America’s chief U.S. economist, pointed out there is a risk the House’s more conservative members could call a vote of no confidence on McCarthy. While that would “gum up the process when timing is running short,” the risk of such a vote is low, he wrote in a note Tuesday. Evercore’s Marcus noted even if McCarthy faces a vote for his removal as speaker, it will likely fail. He expects a “critical mass” of Democrats would abstain or outright support McCarthy to prevent him from being replaced with a more conservative and weaker speaker. “It makes no real sense for Democrats to cooperate with the far right in punishing McCarthy for striking a deal with Biden,” he wrote in a Tuesday note. Tight House vote It’s expected to be a tight vote in the House. A conservative bloc of House Republicans has publicly attacked the bill and several Democrats have also spoken out against it. It’s not clear exactly how Republican and Democratic lawmakers will divide the responsibility for passing this legislation since most likely want it to pass, but few want to vote for it, Goldman’s Hatzius said. The GOP controls the House by a margin of 222 to 213 and the bill needs a simple majority, or 218 votes, for passage, BTIG’s Boltansky pointed out. “The biggest concern in the House is the vote counting operations of Speaker McCarthy (R-CA) and Democratic Leader Jeffries (D-NY) as they are both sitting in new seats and this will be a tight vote in the House,” he said. Conventional wisdom at the time of his Monday note was McCarthy will deliver at least 150 Republican “yes” votes and Democrats should deliver at least 70 “yes” votes, Boltansky said. “The bill is expected on the floor Wednesday evening, but a number of contacts suggest that passage could slip to early Thursday morning,” he said. Slowdown in the Senate? While Boltansky expects the package is likely to receive enough votes to clear the upper chamber, he’s concerned about the timeline. A single senator can “meaningfully slow the process,” he said. “For example, Sen. Mike Lee (R-UT) has said that he will elongate consideration of the package if it does not deliver ‘substantial’ cuts, which could push passage dangerously close to the June 5 deadline even though the ultimate outcome is not in serious doubt,” Boltansky wrote. Hatzius is pegging the timeline for a potential Senate vote by Friday, although he said it could be pushed into the weekend due to delays. “Regardless of the procedural details, with a deal in hand it seems very unlikely that Congress will fail to act by the June 5 deadline the Treasury has projected for lifting the debt limit, though the final bill will probably be enacted with only a few days to spare,” he said. — CNBC’s Michael Bloom contributed reporting.