A $14.4 million tax package that is essential to balancing Mayor Marion Barry's proposed 1984 budget appears headed for defeat next week when it is scheduled for a vote by the D.C. City Council's Finance and Revenue Committee.

Council member John A. Wilson (D-Ward 2), chairman of the committee, said late this week that there are not enough votes in his committee or in the full council to adopt the entire package.

"The mayor's tax package is in deep trouble," Wilson said. He added that while the council eventually may go along with parts of Barry's plan, "under no stretch of the imagination do I think the whole package will fly."

Council members Betty Ann Kane (D-At large) and H.R. Crawford (D-Ward 7), both members of the finance committee, said yesterday that they would oppose the tax package because the administration has not done enough to reduce waste and increase efficiency in tax collections.

"The mayor made a campaign promise not to raise taxes and there's no need to raise them," Kane said. "If we did a better job of collecting money owed us . . . and managing money better, there would be no reason to raise taxes."

Crawford said he has written to Barry to complain that the city wastes large quantities of water, despite a mounting deficit in the water and sewer fund, and has allowed city workers to slough off on the job.

"Until I get some answers from that letter, I'm not going to vote for the tax increases ," Crawford said. "First we have to justify what we're spending, and I haven't seen that."

Council members Polly Shackleton (D-Ward 3) and Hilda Mason (Statehood-At large), the two other members of the committee, could not be reached for comment.

Alphonse G. Hill, deputy mayor for finance, said yesterday he was unaware that the mayor's tax package was in trouble. "I thought we were looking pretty good," Hill said. "Sounds like we better do our homework."

The defeat of part or all of Barry's tax package would throw out of balance the mayor's proposed $1.9 billion budget for the fiscal year that begins Oct. 1.

City officials are feeling pressure from President Reagan's 1984 budget proposal that, if enacted by Congress, would force the city to spend at least $50 million more than Barry has recommended. The increase would come in payments for St. Elizabeths Hospital and retirement benefits.

Barry's tax proposal includes a new gross receipts tax on utilities that would raise an additional$8.2 million, higher motor vehicle registration fees that would net$2.9 million, a new tax on construction in progress that would bring in $1 million and other miscellaneous user charges totalling $2.3 million.

The mayor also has asked the City Council to increase water and sewer service rates by a total of125 percent during the next five years, in order to retire a $35.7 million deficit in the city's water and sewer fund. Another council committee last week recommended a one-time increase of 35 percent, but no subsequent increases.

Wilson said that he intends to introduce several tax increase proposals of his own next week, including one that would increase the yearly charge to newspapers with vending machines on the streets from 50 cents per machine to $25 per machine. He said that he may exempt local newspapers from the proposed fee increase.

Wilson also will propose increasing the business franchise tax and professional license fees, in order to raise $500,000 to buy bullet-proof vests for city policemen. Private businessmen and members of the Fraternal Order of Police recently launched a fund-raising campaign to pay for the vests, but Wilson contends that the city should pay for them.

"It is an embarrassment to our city that our policemen and women must depend on community fund-raising efforts to afford items as vital to their jobs as bulletproof vests," he said.