The answer to this question depends to some degree on what you think your instructor is asking you. Is the instructor asking whether the Supreme Court thinks these programs are constitutional or whether you think they are constitutional?
If you think the instructor is asking for your opinion, then you need to decide for yourself whether you think these programs are legal. Let us look at the arguments on each side. On the one hand, many people think these programs are illegal under the 5th Amendment. The relevant part of that amendment says that you cannot be deprived of your property without the due process of law. Generally, that means that the government cannot take away your property unless you are convicted of a crime. In asset forfeiture programs, the police are allowed to take away your property simply because they believe (based on a preponderance of the evidence) that your property was used to commit a crime or that it was bought with the proceeds of a crime. This would seem to violate the 5th Amendment, making such programs unconstitutional.
However, the Supreme Court has ruled that the programs actually are constitutional. The reasoning here is that the police are not actually acting against you when they seize your property. Instead, they are acting against the property itself. Legally, it is your property, and not you, that is being charged with wrongdoing. What this means is that the property is not being taken away from you as a punishment and therefore does not fall under the 5th Amendment.
So, if your instructor is asking you what the Supreme Court thinks, you have to say that these programs are constitutional. If your instructor is asking what you think, you have to think about these two arguments and decide which one you agree with.
As of August 6, 2015, civil asset forfeiture laws are constitutional because the Supreme Court of the United States has not declared them to be unconstitutional.
Civil asset forfeiture laws are a result of the war on drugs and the Racketeer Influenced and Corrupt Organizations Act, or RICO Act. The war on drugs enabled federal and state law enforcement agencies to hand down indictments on suspected drug criminals, but such indictments had very little effect of drug kingpens were able to keep the millions of dollars in cash and assets that said criminals amassed as a result of criminal activity. With civil asset forfeiture laws, law enforcement agents could also indict your property and money via RICO laws, arguing that your property is also a party to criminal activity.
While very few people complained about such laws when it was only heroin and cocaine kingpins being busted in the 1980s and 1990s, civil asset forfeiture laws have come under considerable scrutiny as law enforcement agencies began abusing these laws by confiscating any and all property of people who were never accused of a crime. There are hundreds of reports of police officers confiscating peoples' cash by claiming that such cash could be used in criminal activities. It is very difficult to get your property back because police departments very often liquidate your assets and incorporate the money into their operating budgets.
While the Supreme Court has consistently ruled 5-4 in favor of existing civil asset forfeiture laws, President Obama and the DOJ have issued memoranda calling for reducing the use of such laws and calling on Congress to clarify the reach of forfeiture laws.