To be fair, Carter had both houses of Congress.
The budgets Reagan submitted to Congress were larger than the ones he submitted, so if anything, congressional Democrats kept his spending in check
Reagan had the Senate for all but the last two years. As for the House, he basically did have it in the form of a Republican+ConservaDem coalition.
To add to that, Carter didn't really have Congress. The congressional Democrats basically hated Carter and worked to undermine him from day one, ending in the Kennedy primary challenge.