President Reagan is proposing to eliminate the Treasury Department's Bureau of Alcohol, Tobacco and Firearms as part of his latest round of budget cuts, agency and congressional sources said yesterday.

In addition, Education Secretary Terrel H. Bell was reported by sources at the National Education Association to have told a meeting of state school administrators his department will be asked to cut $1.5 billion next year and $9 billion by 1984, reducing spending to its lowest level in more than 25 years. But Bell said through a spokesman last night there was no discussion of figures at the meeting.

In addition to the BATF, the Consumer Product Safety Commission was on the White House extinction list, and members of Congress were told of its inclusion earlier this week.

But an administration source said last night that budget cutters decided that elimination of the CPSC would be a mistake in light of Congress' reauthorization of the commission at a reduced level of powers.

As additional details of the new spending cutback plans leaked out, there were signs of mounting opposition on Capitol Hill, including plans for a House Republican counterproposal as well as predictions that the administration program may fail unless it is substantially altered.

"The Republican votes in the House just aren't there the way it is configured now," said a well-placed GOP congressional aide. "I don't think the administration plan is going to get very far," said House Democratic Whip Thomas S. Foley (D-Wash.). "There will be widespread reaction against it, and not just from Democrats."

In the Republican-controlled Senate, Budget Committee Chairman Pete V. Domenici (R-N.M.) acknowledged that there seemed to be "concern about certain aspects of the package and skepticism about whether it can be done," although he noted that members' reactions were based in part on incomplete information. Senate Majority Whip Ted Stevens (R-Alaska) went even further, saying: "I think we ought to wait, even until March, to see how the economy is. . . I would favor waiting until that time to make those new cuts."

House Minority Leader Robert H. Michel (R-Ill.) was reported already to be working with other Republicans on revisions to the roughly $16 billion in new budget cuts for next year that the administration is planning to recommend. These would be on top of $35 billion in cuts already approved by Congress.

The Treasury Department's BATF, which enforces federal gun laws, is among 30 to 40 agencies, boards and commissions that--along with the departments of Education and Energy--have been marked for extinction in the latest round of budget cuts. BATF has been the target of criticism from the gun lobby.

The proposed shutdown of the BATF is "purely a concession to the NRA," said a high-level bureau official, referring to the National Rifle Association. The official added that the net effect will be that gun control laws will be "largely unenforced."

According to other bureau and Treasury Department officials, the Secret Service will absorb agents responsible for control of firearms, cigarette smuggling and arson, and the Customs Service will take agents responsible for control of alcohol. As many as 1,600 of the bureau's 3,500 employes may be fired, sources said.

House Judiciary Committee Chairman Peter W. Rodino Jr. (D-N.J.) said he will review the planned shutdown. "It makes no sense for the administration to dismantle the federal agency responsible for tracking illegal guns and enforcing firearm laws at a time of heightened national concern over violent crime," Rodino said.

While claiming that the NRA has never sought the bureau's extinction, association spokesman Jim Lorell said, "No one is particularly unhappy" with news that the bureau is to be shut down.

"If the plan calls for a reduction in agents, it is certainly surprising given the fact that this administration was supposed to come in to wage a war on crime," said William Nickerson, who was deputy assistant treasury secretary for enforcement during the Carter administration.

On Capitol Hill and at BATF there was speculation that the agency is being eliminated for political as well as budgetary reasons. BATF officials said it has a budget of about $150 million. "You don't think they're doing this as an economy move do you?" asked a congressional staffer, speaking of the BATF shutdown.

Meanwhile, Sen. William L. Armstrong (R-Colo.), chairman of the Senate Social Security subcommittee, said House Democratic leaders probably have killed any chance for a bipartisan Social Security bill this year by their decision to oppose all the president's major Social Security cuts.

Armstrong said, "It would be crazy to put out a Republican bill" both because it would be impossible to pass and because of its political risks. However, Senate Finance Chairman Robert J. Dole (R-Kan.) said he isn't prepared to drop the bill yet. "When they House leaders get through with the fun and games over there, we may be able to work something out."

Staff writers David S. Broder, Spencer Rich, Charles R. Babcock and Mary Thornton contributed to this report.