President-elect Donald Trump’s nominees are headed for brutal confirmation hearings, and his choice of ExxonMobil CEO Rex Tillerson for secretary of state is shaping up to be the most grueling, but history shows that the Senate rarely musters the nerve to reject Cabinet picks.

Only nine Cabinet nominees in U.S. history have been defeated in committee or Senate votes, although 12 others have been withdrawn in the face of strong opposition. The last time a nominee was defeated outright came in 1989, when former Sen. John Tower, President George H.W. Bush’s pick for defense secretary, went down in a party-line vote in a Democrat-majority Senate.

Nearly every one of Mr. Trump’s nominees has encountered objections from Senate Democrats, from accusations that his pick for the Environmental Protection Agency, Oklahoma Attorney General Scott Pruitt, is anti-environment to charges his choice to head the Labor Department, fast-food titan Andrew F. Puzder, is anti-worker.

The expected nomination of former Texas Gov. Rick Perry for secretary of energy met opposition from Democrats and liberal groups that noted he once proposed eliminating the Energy Department.

Mr. Tillerson encountered the stiffest opposition yet, including from several Republican senators who said they share Democrats’ concerns about his close business ties to Russian President Vladimir Putin.

In the past, however, nominations were more likely to be derailed over personality than policy.

Mr. Tower, the only former senator to be denied confirmation in a vote by his colleagues, was rejected amid reports of past drinking problems and claims that it rendered him unfit for office.

Prior to Mr. Tower’s ill-fated nomination, historians have to go back to Dwight Eisenhower’s pick of Lewis L. Strauss for commerce secretary in 1959 to find another confirmation casualty. Mr. Strauss, who played a key role in formulating early U.S. nuclear weapon policy, was known for his prickly disposition, which proved his biggest liability and ultimately undermined his nomination.

In that case as well, a Democratic majority in the Senate denied the Republican president’s choice.

In recent years, it has been more common for a nomination to be withdrawn rather than suffer the humiliation of being voted down. Since 1996 six nomination have been withdrawn: three of Bill Clinton’s, two of George W. Bush’s and one of Mr. Obama’s.

Mr. Obama’s choice for health and human services secretary, former Sen. Tom Daschle, withdrew over questions about his tax returns and his work as a lobbyist, which appeared to contradict the president’s campaign pledge to bring change to Washington. Mr. Daschle’s nomination foundered despite fellow Senate Democrats being in the majority.

Senators revere their constitutional duty of “advice and consent” over nominations, but they also pride themselves on showing deference to presidents in filling their Cabinets. That explains the rarity of nominees being rejected.

But those rules may no longer apply, said political strategist Jim Manley, a former top aide to outgoing Senate Democratic leader Harry Reid. He predicted that at least one of Mr. Trump’s nominations would be defeated or forced to withdraw.

“It’s true in the past that the Senate has struggled to make sure that the president gets the people he asks for to serve in his Cabinet. What I don’t know is whether ‘that was then and this is now,’ because the norms have changed so much,” he said.

Senate Democrats could be looking for retribution against Republicans for denying both a vote and confirmation hearings on President Obama’s nomination this year of Judge Merrick Garland for the Supreme Court. Republicans shelved the nomination for eight months, waiting for the presidential election and the chance a Republican would win and next year name a conservative justice to the high court.

“What they did to Merrick Garland is absolutely, flat out unacceptable. And the question is what kind of impact that is going to have going forward,” Mr. Manley said.

Mr. Trump’s nominees benefit from having his party in the majority, which means Democrats would need Republican votes to block confirmation.

When Mr. Tillerson goes before the Senate Judiciary Committee, he will face 10 Republicans and 9 Democrats.

If Democrats remain united in opposition, it would take just one Republican vote to stall the nomination. However, a straight Democratic Party line then puts incredible pressure on each Republican not to break ranks.

Sen. Marco Rubio, Florida Republican and a member of the committee, said he has “serious concerns” about Mr. Tillerson. Whether he would stand as the lone Republican to deny Mr. Tillerson the post remains to be seen. He promised a “full and fair but also thorough hearing.”

At the same time, Senate Majority Leader Mitch McConnell and Senate Majority Whip John Cornyn announced they would support confirmation of Mr. Tillerson, signaling a consolidation of GOP support.

When the nominations reach the chamber’s floor, Republicans hold a 52-48 majority. If Democrats march in lockstep against a nominee, they will need three Republicans to join them.

Democrats also lost the leverage of the filibuster. When in the majority in 2013, Senate Democrats resorted to the “nuclear option,” changing the chamber’s rules to allow confirmation of President Obama’s appointments with a simple majority rather than the previously required 60-vote supermajority.

The new rules further smooth the way for Mr. Trump’s picks.

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