The advice and consent of the U.S. Senate is proving elusive for the Biden administration as individual senators from both parties, for different reasons, hold up a raft of nominations for everything from foreign ambassadors to U.S. attorneys to EPA administrators.

Senator Tuberville’s one-man campaign to hold up promotions in the military to protest the Pentagon’s abortion policies is getting the lion’s share of attention on Capitol Hill, but similar protests by a number of prominent voices in the Senate also are grinding on and drawing the ire of President Biden and his charges.

In a letter to lawmakers Monday, Secretary Blinken said more than 60 nominations to posts in the foreign service, including 38 ambassadors, are being thwarted in the Senate, and the delays are, as he put it, endangering national security. “Vacant posts have a long-term negative impact on U.S. national security, including our ability to reassure allies and partners, and counter diplomatic efforts by our adversaries,” Mr. Blinken said in the letter.

Mr. Blinken singled out Senator Paul, a Republican of Kentucky, as the main culprit. Mr. Paul has put a hold on all state department nominations in an effort to compel the Biden administration to deliver documents related to the origins of the Covid pandemic. Mr. Blinken said during a rare appearance at the department’s daily news briefing Monday that among the hold-ups are nominations for critical ambassadorial posts in the Middle East as well as a counterterrorism coordinator.

“People abroad see it as a sign of dysfunction, ineffectiveness, inability to put national interests over political ones,” Mr. Blinken said at the briefing. “They’re being blocked for leverage on other unrelated issues. It’s irresponsible, and it’s doing harm to our national security.”

Another roadblock for Mr. Biden is Senator Vance, a freshman Republican of Ohio. Mr. Vance has said he will hold all nominations to positions in the Department of Justice to protest what he called Attorney General Garland’s “political persecution” of President Trump and the politicization of the department.

“Merrick Garland’s department harasses Christians for pro-life advocacy, but allows hardened criminals to walk our streets unpunished,” Mr. Vance said. “This must stop, and I will do everything in my ability to ensure it does. … If Merrick Garland wants to use these officials to harass Joe Biden’s political opponents, we will grind his department to a halt.”

Article II of the U.S. Constitution gives the president power to nominate anyone to just about any post but requires him to do so with the “advice and consent” of the Senate. Most nominations are routinely confirmed, but a single senator with a grudge can withhold that consent by putting a hold on nominations and forcing them to be considered one at a time, taking many hours each.

The senators creating personnel headaches for Mr. Biden are not just Republicans. Senator Sanders, the Vermont independent, is holding up what was considered a slam-dunk nomination to head the National Institutes of Health, Monica Bertagnoli, over a disagreement with the administration over its drug-pricing agenda.

Then there is the bothersome Democratic senator of West Virginia, Joe Manchin. Mr. Manchin said last week that he would oppose Mr. Biden’s nominee to be labor secretary, Julie Su, all but dooming her chances of being confirmed by the entire Senate. Mr. Manchin has also pledged to block all the administration’s nominees at the Environmental Protection Agency, which he accuses of pursuing radical and counterproductive policies in the name of curbing greenhouse gasses and combating climate change.

“This Administration is determined to advance its radical climate agenda and has made it clear they are hellbent on doing everything in their power to regulate coal and gas-fueled power plants out of existence, no matter the cost to energy security and reliability,” Mr. Manchin said. “I fear that this Administration’s commitment to their extreme ideology overshadows their responsibility to ensure long-lasting energy and economic security and I will oppose all EPA nominees until they halt their government overreach.”