The federal Drug Enforcement Administration has run short of funds to reimburse its agents for hotel rooms and meals while out of town; one group of agents in Detroit has been sleeping on rented cots and cooking on a hot plate while on an out-of-town assignment.

A spokesman says the DEA also is starting no new investigations, has restricted travel to court appearances, and in some offices is keeping 50 to 60 percent of its vehicles garaged because of no money for gasoline.

The Bureau of Alcohol, Tobacco and Firearms is also running short of funds. Two weeks ago in Tennessee, the ATF for lack of money backed out of an undercover deal to buy some dynamite and a number of machine guns, and in Florida ATF canceled a deal for a car full of plastic explosives. The administration plans to eliminate ATF over the next few months, but meanwhile the agency employes have been buying gasoline themselves to make court appearances.

All over the country, federal law enforcement officers say they already lack the money to do their jobs. That is without the Reagan budget cuts now taking effect; they say these will make the problem worse.

The agencies and some who support them in Congress find irony in the situation: an anti-crime administration cutting back on anti-crime funds.

Rep. William J. Hughes, chairman of the House crime subcommittee, calls the federal law enforcement funding problems "probably the worst I've seen since I've been involved in law enforcement issues."

The New Jersey Democrat charges that the Reagan administration has been "totally inconsistent. Instead of supporting the fight against crime, they are retreating." The Democratic National Committee has sent out material to likely 1982 candidates, urging them to capitalize on the issue.

The agencies have sent the Office of Management and Budget analyses of how the appropriations cuts the president proposed in September would affect them in the current fiscal year. These have leaked out as the agencies have worked in traditional ways to forestall the cuts.

President Reagan proposed in September that appropriations for most agencies be reduced 12 percent below the levels he first recommended in March. For a few agencies such as the FBI he proposed lesser cuts. He has since backed down from these September proposals somewhat, but at the same time OMB is considering further cuts for fiscal 1983.

During the 1981 fiscal year, the FBI had a budget of $683 million. In March, Reagan proposed raising it to $739 million but the administration in September revised that request downward to $694 million. The DEA budget was $216 million last year, the March figure was $228.5 million, and the latest request is $201 million. For ATF, last year's budget was $150 million, the March request was $155 million, and the latest request was $120 million, a cut of 20 percent.

The FBI has already put a freeze on hiring and restrictions on travel. Reagan's September proposal that it trim spending an additional 6 percent would cause "serious problems," a bureau source said yesterday.

The analysis prepared by the bureau for OMB says the bureau would have to fire the equivalent of 1,006 full-time employes, more than 5 percent of its total. It adds that "probably no new undercover operations will be authorized" in fiscal 1982 against organized crime or white-collar crime.

A cutback of nearly one third in FBI investigations of gambling, prostitution, arson for profit, gangland slayings and pornography would be required.

In addition, there would be major cutbacks in training of agents, in funding for FBI labs and in the fingerprint identification section. Those cutbacks would hurt not only the FBI but also state and local law enforcement agencies that depend on the bureau for assistance.

DEA already has severe problems, and the president proposed a further 12 percent budget cut for it in the current fiscal year.

Attorney General William French Smith, who has supported most of the budget cuts, interceded on behalf of DEA last week for enough money to make it through this week, but agents say that their investigations are a shambles because of funding inconsistencies that have caused informants to go unpaid and deals to be broken off at the last minute.

A federal magistrate in Fort Lauderdale recently had to release a major drug offender because the DEA office in New York did not have the money to send an agent down to identify him.

In Detroit, Joe Salvamini, DEA's special agent in charge, says his agents are trying to work undercover in cars with broken headlights and loose mufflers because there is no money for repairs. Agents have gone so far as to take cars home to change their oil, a violation of government regulations.

"Have you ever tried to tail someone with a broken headlight? You know what it's like trying to work undercover with a loose muffler?" he asked.

Acting DEA administrator Francis Mullen told a Senate subcommittee this week that a 12 percent cut would "cripple the agency." Mullen said the proposed budget for 1982 is less than 1980's.

The analysis for OMB indicates that at least 392 jobs, or 10 percent of DEA personnel, would be eliminated. In addition, employes would be required to take two-week furloughs without pay to reduce expenses. Travel would be reduced 25 percent and major cuts would be made in funds for purchasing evidence and paying informants.

Under the proposed cuts, DEA would have to close 24 of its small regional offices. Funding for three-fourths of the state and local task forces, described as one of the most successful programs at DEA, would be eliminated.

The analysis says DEA would completely shut down 12 of the task forces, including those in New York, Chicago, the District of Columbia, Philadelphia, St. Louis, San Diego and Minneapolis. Three of those cities, New York, D.C. and Philadelphia, are classified by DEA as having some of the most severe heroin problems in the country.

There would also be major cuts in intelligence operations, in the chemical labs, in training and in technical equipment including aircraft, radio equipment, and wiretapping equipment.

Hughes is holding hearings to look into the cuts, particularly the disbanding of ATF, where at least one third of the 3,400 employes are expected to be fired with others being reassigned to the Secret Service and the U.S. Customs Service. "They're the only agency with expertise in handgun tracing, arson and explosives, and their capabilities are being totally undermined."

Hughes is also concerned about a 12 percent cut in Coast Guard funding that he says is hampering drug enforcement. "Ninety percent of the Pacific coast operation in drug interdiction has been phased out," he said.

Both the House and Senate are attempting to increase appropriations for law enforcement above what Reagan has requested, but the president has threatened to veto legislation that violates his budget.