WASHINGTON — House Democrats on Monday presented a plan to pay for their expansive social policy and climate change package by raising taxes by more than $2 trillion, largely on wealthy individuals and profitable corporations.

But the proposal, while substantial in scope, stopped well short of changes needed to dent the vast fortunes of tycoons like Jeff Bezos and Elon Musk, or to thoroughly close the most egregious loopholes exploited by high-flying captains of finance. It aimed to go after the merely rich more than the fabulously rich.

Facing the delicate politics of a narrowly divided Congress, senior House Democrats opted to be more mindful of moderate concerns in their party than of its progressive ambitions. They focused on traditional ways of raising revenue: by raising tax rates on income rather than targeting wealth itself.

Representative Dan Kildee of Michigan, a Democrat on the Ways and Means Committee, which crafted the plan, called it “the boldest common denominator.”