The struggle of Senate Democrats and the Reagan administration for the last word in treaty-making has unexpectedly widened the debate over the new U.S.-Soviet nuclear arms accord into a contentious confrontation that is sending tremors through both parties.

The tussle has caused cleavages within Democratic and Republican ranks and caught the administration in a difficult squeeze, attempting to placate powerful Democratic leaders without offending its most loyal conservative Republican adherents.

Senate Armed Services Committee Chairman Sam Nunn (D-Ga.) has thrust himself once again to the forefront of arms-control maneuvering, leaving the administration and Democratic majority on the Foreign Relations Committee in disarray.

The controversy raises anew a possible outpouring of amendments, reservations and other conditions that could delay and complicate Senate approval of the treaty to eliminate intermediate-range nuclear forces (INF), some senators warn.

A prolonged treaty debate could cut into other Senate business, hurting the Democratic-controlled Congress' hopes of showing voters in this fall's elections what a Democratic government would give the country.

Democrats, who once could argue that only dissident Republicans might hold up the pact, now face GOP accusations of jeopardizing early INF approval with a "domestic political power play."

Republicans are angry with the administration over its moves to compromise with the Democrats; some suggest the administration may be sorry the next time it counts on them to "fall on our swords" for the White House on the Senate floor.

The State Department, said a Senate Republican leadership aide, has "seized the opportunity to anger everyone . . . and has taken us back to Square One without really resolving anything."

The dispute dates to 1985 when the administration, attempting to reinterpret the 1972 Antiballistic Missile (ABM) Treaty to allow advanced testing of its controversial "Star Wars" missile defense system, asserted that administration testimony at ratification hearings may not reflect a treaty's true meaning.

Democrats contended this would enable presidents to reinterpret treaties to suit their purposes without Senate consent, and now are trying to use the INF debate to resolve the treaty-interpretation issue in the Senate's favor.

But there are splits. While Nunn tries to extract concessions from the administration, Sen. Joseph R. Biden Jr. (D-Del.), second-ranking Democrat on the Foreign Relations Committee, wants to attach conditions to the INF Treaty that would, in effect, write into law what Democrats regard as the Senate's historic powers in treaty-making.

Secretary of State George P. Shultz has sent a letter to Nunn and Majority Leader Sen. Robert C. Byrd (D-W.Va.) addressing their concerns, but neither the letter nor Biden's proposal scores a direct hit on the administration's "broad" ABM treaty reading, which is what most Republicans and Democrats care most about. But, because both could give Democrats ammunition for that fight, Republicans worked yesterday to get a Shultz letter of their own to foreswear any implications for future debates over ABM and the "Star Wars" Strategic Defense Initiative (SDI).

They are also laying longer-range plans to fend off Biden.

Biden remains unsatisfied, saying that regardless of assurances from Shultz, Biden will meet early next week with Byrd and Nunn in hopes of enlisting them in his cause.

Acknowledging surprise at the Nunn-Byrd threat to hold up INF hearings until the treaty-interpretation dispute was resolved to Democrats' satisfaction, Biden said, "It was kind of unfortunate that it occurred."

Biden expressed fear that the partisan response to the Nunn-Byrd move could undercut chances for the bipartisan support he wants for his move.

Meanwhile, Senate Republicans are "seething," as one source put it, over Shultz' attempt to conciliate Nunn.

"The administration had a chance to slam-dunk Sam Nunn and lost it," complained one senior GOP aide.

Few senators interviewed in the past two days expressed fear the dispute jeopardizes Senate INF Treaty approval. But some said it could delay action on ratification by "opening the floodgates" for amendments and reservations on other issues.

"My fear is there could be a chain reaction . . . . It gives treaty opponents an opportunity to raise problems and then blame the other side," said Sen. Arlen Specter (R-Pa.), a moderate who joined conservatives to urge Shultz against making concessions to the Democrats.

But others said they believe both sides have too much at risk to let the dispute get out of control.

"If people are still waiting in August for that treaty they heard such good things about in January, there will be hell to pay," one Senate staffer said.