The Contender (2000) on Netflix

After his Vice-president suddenly dies, the President (Jeff Bridges) who is near the end of his final term, decides to leave a legacy by selecting a woman to fill the position. Enter a Senator (Joan Allen), who has shifted from the Republican Party to the Democratic. Initially appearing to be the perfect candidate, an allegation suddenly appears that she had been involved in a sexual orgy as a 19 year old in college. The confirmation committee chairman (Gary Oldman), a Republican, leaks the information to the press, while using the press discussion as a forum to bring it into the hearings. The chairman desires to get a Governor (William Petersen) into the office. The Governor had become a national hero when he attempted to rescue a young woman from a car that crashed from a bridge into deep water near where the Governor had been fishing.