WASHINGTON — For years, the White House saw House Majority Leader Eric Cantor as a chief driver of Republicans’ staunch opposition to nearly all of President Barack Obama’s agenda. Now, Cantor’s stunning primary loss seems likely to make politics even more difficult for Obama.

Rather than opening a pathway for the president, Cantor’s defeat could push Republicans more to the right and harden the House GOP’s hostility toward the White House, virtually dooming Obama’s efforts to pass a legacy-building immigration bill or other major legislation.

Robert Gibbs, a longtime Obama adviser, said any glee at the White House over Cantor’s defeat was “quickly replaced by the reality that this is the end of anything productive getting done legislatively in Congress either this year or maybe for the next several years.”

Cantor, the No. 2 Republican in the House, was soundly defeated by his tea party-backed opponent, a little-known economics professor named David Brat, in Virginia’s GOP primary Tuesday. Despite being massively outspent by Cantor, Brat rode a wave of public anger over calls for more lenient immigration laws, reducing the prospects that already reluctant House Republicans might take up a bill this year.