WASHINGTON — By agreeing to delay Judge Brett M. Kavanaugh’s nomination in the short term, President Trump and Senate Republicans are making two long-term bets: that a drawn-out confirmation battle will secure a conservative majority on the Supreme Court, and that the fight will give them a better chance of keeping control of the Senate in the midterm elections.

With that Senate majority squarely in mind, Republicans are also making a concession to stark political realities. Party leaders have concluded that supporting Judge Kavanaugh’s nomination, in the face of sexual assault accusations against him, will all but ensure that Republicans lose control of the House in November even as their fortunes may improve in some tough Senate races.

The thinking, according to Republicans, is that Judge Kavanaugh’s confirmation would cause a backlash from female and independent voters against Republican candidates in dozens of highly competitive House races — many of which have already been slipping away — and do more damage than in statewide Senate contests. The party has a 23-seat majority in the House.

Even as Mr. Trump and Senate leaders acceded to an F.B.I. investigation into the accusations against Judge Kavanaugh, Republicans say they did so grudgingly. Privately, they are determined to press ahead with the confirmation process despite the political risks and the possibility that Republican senators may still defect and oppose the nomination in the end.