Washington — While most Republicans ran for cover when news of the President's budget deficits hit, the man whose tax cutting bill is blamed for much of the red ink remains undaunted. And he predicts that Mr. Reagan will have his party's support on the budget.
''I think the President has been courageous in attempting to maintain the thrust of his budget and fiscal policy,'' US Rep. Jack Kemp (R) of New York said last week to a conservative economics conference.
Congressman Kemp, who pushed for and won massive personal tax cuts last year, says, ''I don't agree with every dotted 'i' in the budget.'' He complains, for instance, that the Reagan budget does not cut ''corporate welfare,'' such as the synthetic fuel program.
But overall he supports the budget, and, he predicts, so will his Republican colleagues in the end. ''The alternative is so indigestible,'' he maintains, pointing out that the only other budget proposal so far is Sen. Ernest F. Hollings's suggested freeze on all spending and tax cuts. Others in the Republican leadership have publicly praised the Democratic senator's plan, but Kemp charges that the Hollings freeze would guarantee a drastic drop in economic growth.
''The Reagan plan is going to look better as people look at the alternatives, '' says Kemp, who ranks No. 2 in the House minority leadership. Asked about the Democrats, he adds, ''They don't know what to do. They want to reduce the deficit, but they don't want to reduce spending.'' And, says Kemp, that means raising taxes.
A spokesman for the Democratic-controlled House Budget Committee concedes that raising taxes is the way to bring the deficit down. Such a plan would be so politically risky that it would require backing from both parties, he says.
Minority leader Robert H. Michel (R) of Illinois has set a meeting this week with Budget chairman James R. Jones (D) of Oklahoma to discuss a possible bipartisan effort.
However, an aide strenuously rejects the notion that the Republican leader is turning against President Reagan. Congressman Michel has shown open interest in the Hollings plan and decried the almost $100 billion in projected deficits. But his aide says, ''Mr. Michel is not running away from the President and is supportive as much as he can be, given the political circumstances.''
''He still thinks you can pass a budget that without reservation can be called a Reagan budget,'' says the aide, explaining that Michel liked the Hollings proposal only because the senator proposed reductions in entitlements, including social security and federal pensions.
Michel is apparently upset over a growing number of letters asking him why he isn't supporting the President. ''It's alarming because he is supporting the President,'' says the aide.
Republicans who are publicly showing new-found independence from the White House may not be straying for long. One congressional observer notes that ''everybody's looking for maneuvering room'' and that Republican leader Michel is ''appearing to be doing battle overtly'' to make room for members who want to stay with the President.
Meanwhile, ''supply-sider'' Kemp, who is less involved with building a coalition for the President, appears little worried over deficits, which he portrays as ''investments'' in the future.
He readily admits that the tax cuts he helped foster, plus the recession, are boosting deficits. But the tax cuts ''will feed back into economic growth,'' Kemp says.
But the fly in the ointment remains high interest rates that hold back economic growth. Kemp blames the Federal Reserve for keeping rates high as a cure for inflation.
In this area, he moves sharply away from President Reagan, who Feb. 18 pointedly endorsed the Fed, saying, ''The administration and the Federal Reserve can help bring interest rates down faster by working together than by working at cross purposes.'' Also of note from Capitol Hill . . .
* Stockman status still in doubt
Still up in the air is whether Budget Director David A. Stockman will be able to lead the President's budget fight after an article in the December issue of Atlantic Monthly quoted him as having doubts about the economic program he so articulately defended.
Privately, some on the Hill say he will not stay. But many Republicans would like to keep Mr. Stockman. No one knows the budget as well, and no one has made a better witness.
The embattled budget director, his hair freshly trimmed and his reactions carefully under control, faced his first day of grilling last week in the House Budget Committee.
True to his usual form, he spilled out facts and figures without benefit of notes and appeared to have an answer for every question and a justification for every cut. He left the door open for some compromises, especially in corporate tax provisions, and would not reject the possibility of some defense cuts.
* Senate delays Williams decision
Harrison A. Williams Jr. (D) of New Jersey, sentenced to three years in jail for an Abscam bribery conviction, will hold onto his Senate seat for at least another week. His doctor has written that Senator Williams was not well enough to attend the expulsion hearing this week. It has been reset for March 3.
* Congressmen visit El Salvador
* During the legislative break, several congressional delegations visited El Salvador for a firsthand look at internal strife there. Their findings can be expected to produce more controversy over aid for that country when Congress reconvenes.