The last remnants of opposition to the MX missile collapsed in the House yesterday as members agreed to spend $875 million on research and development of a long-term basing system for the new missiles, which is nearly three times as much as the Reagan administration had requested.

The vote puts the House in the position of authorizing $1.14 billion to build MX missiles and a total of $2.6 billion for research and development for them when President Reagan still hasn't decided where to put them. He promised last week that he will decide by December.

Under amendments to the 1983 defense authorization bill yesterday and last week, however, $974 million of the research and development funds that are related to basing cannot be spent until Reagan makes the decision.

The issue will be resolved in conference committee because the Senate cut $1.9 billion from the basing program, which has sparked a controversy over how the missiles can be made invulnerable to Soviet attack.

Reps. Bill Green (R-N.Y.) and Paul Simon (D-Ill.) abandoned efforts to delete entirely much of the $974 million, $715 million for a now-discredited program to put the MXs in existing Minuteman silos. A phalanx of Armed Services Committee members, led by Rep. Les Aspin (D-Wis.), argued that even though the money is technically designated for the Minuteman silo program, it would eventually be needed for the permanent basing program.

The $875 million for long-term basing research and development includes the $715 million plus $160 million earlier earmarked for the program--a cut of Reagan's original request for $310 million for long-term basing research.

Rushing to finish the bill, which has been caught up in a series of controversial debates since early last week, the House approved on voice vote a host of amendments including provisions to:

Require the use of American-mined coal at U.S. bases in Europe, a measure sponsored by Republican Paul Trible, who is running for the Senate in the coal producing state of Virginia.

Prohibit the use of funds to lease tankers containing major components made outside the United States, a measure sponsored by Aspin.

Forbid spending on any new studies to contract out to private employers services now performed by government workers. The measure, sponsored by Rep. Vic Fazio (D-Calif.), would essentially halt in its tracks a long-term policy to let private firms handle services such as laundries and catering.

Businessmen say they can accomplish many Defense Department functions for less than civil service workers can do the job. Government workers, however, counter that work performed by private contractors is often poorly and inconsistently handled.

The House also rejected an amendment by Rep. David F. Emery (R-Maine) that would prohibit funds from being spent on an underground basing system for the MX. Emery said that if the missiles are underground, it would take as long as two to four days to dig them out to counter a Soviet attack.

Aspin, however, argued that underground missiles could be used for backup.

The sudden passage of a half-dozen amendments in a half-hour last night, after three hours of languorous debate on the Simon-Green MX proposals, had the effect of whizzing the House through several entire titles of the bill, thus apparently preventing the consideration of several key amendments, including a proposal to cut funds for civil defense. Provision of funds for civil defense is opposed by nuclear arms foes, who say it will encourage the belief that nuclear war is survivable.

Civil defense opponents called the last-minute maneuvering "sleazy" and got an agreement from House Speaker Thomas P. O'Neill Jr. (D-Mass.) to bring up the amendments that were ruled out of order.