(NewsNation) — House Speaker Kevin McCarthy, R-Calif., has promised to push to get major spending bills to come in under the limit agreed to in debt limit negotiations with the White House.

Rep. Ralph Norman, R-S.C., told NewsNation’s Joe Khalil that McCarthy made the promise to members of the ultraconservative House Freedom Caucus. McCarthy said he would push to get all 12 major spending bills under the agreed-upon limit.

The promise came after members of the Freedom Caucus revolted, blocking activity on the House floor in response to the debt limit deal McCarthy negotiated with President Joe Biden.

Conservative hardliners felt McCarthy gave away too much in the negotiations, particularly when it came to spending limits for which the party was pushing. By reaching a deal, McCarthy and the White House narrowly avoided a default that could have had catastrophic effects on the U.S. and global economies.

McCarthy’s ability to balance the demands of far-right Republicans and more moderate members of the party has come into question. It took 15 votes before he was elected speaker and the revolt has made it clear that some members of his party are willing to use whatever leverage they have to achieve their goals.

If McCarthy holds to his promises and cuts spending bills below the amounts agreed upon, it could lead to a government shutdown in the fall, when Congress will need to pass that legislation to keep the government running.