WASHINGTON—Republican candidates for president are pledging to shut down federal agencies if they win the White House. There is almost no chance they will succeed.

Closing a government agency requires action by Congress. Convincing a majority of the House and Senate to close down agencies, many of which distribute billions of federal dollars to their states and districts, has proven nearly impossible for decades. While past presidents have reorganized and rebranded departments, Washington has never shut down a major cabinet-level agency, according to experts who follow the issue.