Washington — If domestic political pressure for a nuclear arms freeze continues to gather steam, President Reagan will be under great pressure to produce an arms control agreement with the Soviet Union by the end of his first term in office.
Added to that pressure is a plethora of new and old ideas on arms control coming from potential contenders for the Democratic presidential nomination, among them Sens. John Glenn of Ohio and Gary Hart of Colorado.
Churches are becoming increasingly vocal in their criticism, too. A majority of Roman Catholic bishops meeting here, for example, remain unpersuaded by Reagan administration arguments in defense of the US strategy of nuclear deterrence.
President Reagan will have an opportunity to take the initiative to a degree in a long-planned speech on arms control which he is now tentatively set to deliver on Nov. 22. The President is expected to call for US-Soviet agreement on a number of measures designed to guard against surprise, miscalculation, and an outbreak of war by accident.
One idea under consideration is to strengthen the hot-line teletype communications link between Washington and Moscow. The President is also expected to propose more advance warning of missile tests and a broadening of the exchange of strategic data between the two sides.
None of these ideas constitutes a major step toward arms control. The United States already has a 1971 agreement with the Soviets on measures to reduce the risk of an outbreak of nuclear war. It includes advance notification of any planned missile launches beyond the territory of the launching nation and in the direction of the other. The two sides agreed in 1963 to establish the original hot line and agreed again in 1971 to improve that communications link.
But as one administration official explained it, the new measures that President Reagan is expected to propose would first of all send a ''signal'' of goodwill to the new leadership of the Soviet Union and second show that in the absence of a major breakthrough in arms control, ''we can still reach agreement on small measures aimed at preventing tensions from building.''
''The hot line hasn't been used much - fortunately,'' said the official. ''But we could expand both the technology and the utility of it.''
Reagan administration officials say that the Roman Catholic bishops, who met here Nov. 15-18 as well as the advocates of the nuclear freeze movement, may be undercutting Washington's negotiating position vis-a-vis the Soviet Union. The officials say they believe that if the Soviets see pressure building on President Reagan to modify his position on nuclear strategy, on arms control, and on the US military defense buildup, it will cause Moscow to hold off making any significant arms control concessions.
On Nov. 16, President Reagan's national security adviser, William P. Clark, sought to defend the administration's nuclear strategy in a lengthy letter to Archbishop Joseph L. Bernardin of Chicago, chairman of the National Conference of Catholic Bishops' Committee on War and Peace. Mr. Clark charged that the committee's latest draft of a pastoral letter on war and peace ignores the Soviets' military buildup, ''continues to reflect fundamental misreadings of American policies, and continues essentially to ignore the far-reaching American proposals which are currently being negotiated with the Soviet Union. . . .''
Clark said that support from the bishops for President Reagan's arms control proposals would ''add to Soviet incentives'' to agree to the nuclear arms reductions that the US is seeking.
But an informal survey showed that two-thirds of the 285 bishops who are members of the national conference agreed with the essentials of the draft pastoral letter which calls for a verifiable nuclear freeze and rules out the first use of nuclear weapons. The US and its allies have reserved the right of first use of nuclear arms in Western Europe in order to deter the Soviets and offset their superiority in conventional weapons.
Although no one is saying so openly, some administration officials hope that Pope John Paul II might yet have some influence modifying the position taken by the American bishops. Their position has struck many observers as remarkable, because for many years a majority in the Catholic Church hierarchy strongly supported US defense policies.