WASHINGTON — The Supreme Court appeared reluctant Wednesday to allow police to routinely order blood tests for unwilling drunken-driving suspects without at least trying to obtain a search warrant from a judge.

The court heard arguments Wednesday in a case about a disputed blood test from Missouri, against the backdrop of a serious national problem of more than 10,000 deaths from crashes involving alcohol-impaired drivers in 2010, about one every 51 minutes.

That number has dropped by 60 percent in the past 20 years because of a sustained national crackdown on drunken driving. Lawyers for Missouri and the Obama administration argued that dispensing with a warrant requirement would further that effort because any delay in testing a suspect’s blood-alcohol content allows alcohol to dissipate in the blood.

“Here, police are facing the certain destruction of blood-alcohol evidence,” Justice Department lawyer Nicole Saharsky said.

But justices across the ideological spectrum questioned whether the intrusive procedure of sticking a needle in someone’s arm to draw blood should routinely be done without the approval of a judge. At the same time, they made clear that they did not want to unduly delay the collection of blood samples.

Justice Antonin Scalia asked, “Why shouldn’t that determination be made case by case? … And if it would have taken too long, then it’s okay without a warrant. If it wouldn’t have taken that long, it’s bad.”

Wednesday’s case stemmed from the arrest of Tyler McNeely in rural Cape Girardeau County, Missouri. A state trooper stopped McNeely’s speeding, swerving car and the driver, who had two previous drunken-driving convictions, refused to submit to a breath test to measure the alcohol level in his body.

He failed several field sobriety tests and the arresting officer, Cpl. Mark Winder of the Missouri State Highway Patrol, said McNeely’s speech was slurred and he was unsteady on his feet.

There seemed little dispute that Winder had enough evidence to get a warrant for a blood test, but chose not to. Instead, he drove McNeely to a hospital. A technician drew blood from McNeely, who was handcuffed throughout the process.

McNeely’s blood-alcohol content was .154 percent, well above the .08 percent legal limit.

But the Missouri Supreme Court upheld a lower court order that threw out the results of the blood test. The state high court said the blood test violated the Constitution’s prohibition against unreasonable searches and seizures. Police need a warrant to take a suspect’s blood except when a delay could threaten a life or destroy potential evidence, the court said.

About half the states already prohibit warrantless blood tests in all or most suspected drunken-driving cases.

As they tried to figure out how to draw a line between what is reasonable and what is not, several justices asked about other tests for measuring alcohol content, including the familiar breath analysis test and urine samples.

“One of the things that I think affects the view in this case is it’s a pretty scary image of somebody restrained, and, you know, a representative of the state approaching them with a needle. But I take it you would say you need a search warrant for a urine sample, too?” Chief Justice John Roberts asked McNeely’s lawyer, the American Civil Liberties Union’s Steven Shapiro.

Shapiro said the court already has upheld a warrant requirement for urine samples in other contexts. Shapiro also said he believes warrants probably are necessary for breath analysis tests, too, but the court has never ruled on that.

All 50 states have measures known as implied-consent laws that require drivers who are arrested on suspicion of driving while drunk to consent to a blood alcohol test. Refusal to do so generally leads to suspension of a driver license. In addition, prosecutors can use the refusal against a defendant at trial.

In Missouri, a driver who won’t agree to either a breath or blood test can have his license suspended for a year. The ACLU said that the suspension is only 30 days for drivers with no previous convictions who take the test and are found to be impaired.

McNeely may have had more reason than most to object to taking the test. Assistant county prosecutor John Koester said McNeely faced a felony charge with a maximum prison term of four years because of his two prior convictions.

A decision is expected by summer.

The case is Missouri v. McNeely, 11-1425.-

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