President Reagan faces bipartisan surgery on his budget unless he can show either that it will lead toward declining deficits or that it has public support even though it means higher deficits, Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) warned today.

Domenici's warning, coupled with a bid by House Majority Leader James C. Wright (D-Tex.) for inclusion of Democrats in presidential budget planning, came as House and Senate budget leaders gathered for a two-day seminar here in search of ways to shore up what many of them see as an overburdened, endangered congressional budget-control process.

They found little to comfort them, aside from a warm fire, good food and the camaraderie of shared budget miseries at this handsome lakeside resort at DeGray State Park. Not only was their midwinter Sun Belt retreat suddenly snowbound, but the budget outlook was at least as gloomy as it had appeared before Congress adjourned last month.

"If I were a betting man, I'd have to bet it [the strain] would be too much for the process to endure," said Rudolph Penner, an economist for the American Enterprise Institute, citing soaring deficit projections and rebounding interest rates as contributing factors to strains on the budget and on congressional efforts to control it.

Penner was not alone in expressing concern that the 8-year-old budget process was in danger of collapsing under the weight of economic pressures.

Domenici, in a conversation with reporters, worried aloud that, although last year's budget retrenchment was "not as onerous as one might have thought, I think we're getting very close to a perception -- and perhaps a reality -- that it's not fair."

Wright noted that in his Fort Worth congressional district local tax increases caused by cutbacks in federal aid already have eaten up most of the federal tax cuts that Congress approved last year.

Even Florida is sharing in the Frost Belt's credit woes, a congressional aide said. Although Florida's economy normally profits from refugees from the North, people in the North can't find buyers for their homes and thus can't buy retirement property in Florida, the aide said.

The seminar is being sponsored by the fledgling Committee for a Responsible Federal Budget, which was set up last year by two retired budget committee chairmen, former representative Robert N. Giaimo (D-Conn.) and former senator Henry Bellmon (R-Okla.) to provide support from outside Congress for the budget process.

But the process has become so intertwined with Reagan's economic initiatives that the substance of the 1982 legislative agenda never was far from the participants' minds.

Wright was the first to sound the bipartisan theme with a call to Reagan to draw Democratic leaders into his economic planning. "If the president were desirous of... mutual cooperation with the elected Democratic leaders, we would be more than pleased to sit down with him to seek avenues of action toward our mutual goals," Wright said.

Later Domenici said that unless deficits start "moving dramatically downward" or unless Reagan musters the kind of public support he had last year regardless of the deficit numbers, "then a truly bipartisan approach to the first [budget] resolution -- even if it differs substantially from the president's proposals -- is absolutely imperative."

Domenici told reporters afterward he wasn't signaling an impending rebellion but simply "stating the obvious," meaning that congressional Republicans would have to look to a bipartisan consensus if Reagan can't put together one on his own.

Wright said he thought there was a good chance for such a bipartisan consensus. But aside from agreement on closing some tax loopholes such as the sale of corporate tax breaks and getting some savings from defense, there appeared to be little initial agreement.

Wright, for instance, talked about saving $68 billion by reducing and deferring future installments of last year's individual income tax cuts for individuals, while Domenici said, "I'm not even in that league."

Moreover, Domenici was arguing for substantial cuts in basic benefit entitlement programs, while Wright said he opposes deep entitlement cuts.