Congressional Republican leaders warned yesterday, after meeting with President Reagan, that any major "tinkering" could sabotage the administration's offer of $4.3 billion for jobs and recession relief.

But Democrats continued to push for at least some expansion of the plan. Senate Appropriations Committee Chairman Mark O. Hatfield (R-Ore.) weighed in with a jobs proposal of his own, and Republican leaders predicted that there will be follow-up jobs legislation of some kind later this year.

The Republicans' warning--and the Democrats' response that no sabotage is intended--came as both sides worked toward a jobs compromise which may be hammered out in a meeting today between House Democratic leaders and administration aides.

The Democrats were said by an aide to be pushing for "about $5 billion," including new money for summer jobs for young people, fuel assistance for low-income families and health aid for mothers and infants.

After an hour-long meeting between Reagan and key congressional Republicans, Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) noted that these programs were not part of the original administration offer, and warned, "I think almost surely the addition of major new funding levels of that type would sabotage the package." With House Minority Leader Robert H. Michel (R-Ill.) seconding his sentiments, Baker added that "the basic challenge is whether we can keep it as a package and resist the recurring temptation to build on it, add to it, pump it up or make it a Christmas tree."

However, Michel said a "second package" will be presented for action later in the year by a House GOP task force that he appointed to work on jobs legislation before the administration made its offer to House Democrats.

Baker, while saying he does not foresee another big jobs package, told reporters later, "We haven't said every word we're going to say on jobs this year," implying further legislation piecemeal.

"I would emphatically reassure him we have no intention of sabotaging the package," said House Majority Leader James C. Wright Jr. (D-Tex.), adding that the White House expected the Democrats to make some counterproposals.

Acting independently of the White House and the Republican leadership, Hatfield called a news conference to outline his jobs plan. The $4.4 billion includes some of the extra money sought by the Democrats as well as accelerated public works spending in the administration's offer.

At the White House, Michel said the administration offer would create "under a half-million jobs" and added somewhat sardonically, "As a matter of fact, that blip of four-tenths of 1 percent in the unemployment rate from 10.8 percent to 10.4 percent last month created far more jobs than we're going to be able to create in this package we're talking about."

If the House can finish its work in two weeks, as both Michel and Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) have suggested, the Senate can wind up in another two weeks and get the bill to Reagan's desk by the end of March, Baker said, calling that "breathtaking speed for the Congress." CAPTION: Picture, Sen. Mark O. Hatfield (R-Ore.), acting independently of GOP leaders, tells reporters about his $4.4 billion jobs plan. By James K.W. Atherton--The Washington Post