Although aimed primarily at Western Europe, President Reagan's speech on arms reductions yesterday also evoked warm praise from both Democratic and Republican politicians in this country.

From House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) to the most conservative Republicans in the Senate, plaudits for Reagan's address echoed around the Capitol. Howard H. Baker Jr. (R-Tenn.), the Senate majority leader, called the address "historic" and said it would have "a profound effect on foreign policy, not only of the United States, but of the world."

Reagan's speech appeared to serve him well on several fronts, at least initially. It allowed him to retake the political initiative at a time when his administration has been in difficulties; it also enabled him to please congressional hawks while disarming others who have been critical of the administration's previous bellicosity.

The political reaction to Reagan's proposal to swap future deployment of medium-range ballistic missiles in Europe for removal of existing medium-range Soviet missiles echoed the strong support given to President Carter 4 1/2 years ago when Carter suggested "deep cuts" in both superpowers' nuclear arsenals. The Soviets never liked that idea, but it was a great political success in Washington, where hawks and doves, Democrats and Republicans applauded it.

That same broad cross-section emerged yesterday in support of the new Reagan proposals. Skeptical comments were rare. One came from Sen. Gary Hart (D-Colo.), a member of the Senate Armed Services Committee and a staunch advocate of SALT II, the strategic arms limitation treaty that Reagan has shelved.

Hart said the Reagan plan was "bold and far-reaching," but added that "our partners in NATO don't think we are serious about curbing these medium-range weapons," and that it might take a new NATO summit meeting to get Western unity on the subject.

Other Democrats associated with arms control efforts in the past were generous with their praise. Sen. Alan Cranston (D-Calif.), the minority whip, called the new Reagan ideas an "excellent, bold proposal that should lead to serious negotiations." Cranston cautioned, however, that he did not expect the Soviets to accept this initial U.S. proposal, just as the United States would not accept an opening Soviet position.

Said Sen. Edward M. Kennedy (D-Mass.): "I welcome President Reagan's interest in arms control. I hope the administration will at long last pursue truly serious negotiations on intermediate-range missile forces in Europe and on strategic nuclear and conventional arms."

Rep. Jim Leach (R-Iowa), an outspoken Republican moderate who has been sharply critical of the Reagan administration in the past, said, "President Reagan has delivered the most important speech of his life and perhaps of any modern American president."

Conservative Republicans gave unreserved support to the Reagan initiative. Sen. Gordon J. Humphrey (R-N.H.), for example, called it "a smart move." Sen. Jake Garn (R-Utah) said, "This is an opportunity for the Soviets to put up or shut up." Sen. John G. Tower (R-Tex.), chairman of the Armed Services Committee, called the speech "a very fine message" that should convince Western Europe of American sincerity in seeking arms reductions and that "knocks the props out" from under "peace advocates" in the NATO countries.

The possibility that the Reagan proposal was primarily intended as a propoganda ploy annoyed Rep. Samuel S. Stratton (D-N.Y.), a leading hawk on the House Armed Services Committee. Stratton told the Associated Press, "I rather gather. . . that this is really supposed to be a propoganda ploy against the Soviets." He added that he "would be very skeptical that this would do anything to change the views of the pacifists" who have mounted huge demonstrations against new American missile deployments in Europe.