Washington — The Reagan tax-increase package has shaken conservatives in both parties. And although, as some Reaganites contend, conservatives have no other place to go, there's no guarantee that Mr. Reagan will ever again find his old, hard-core constituency automatically responding to his calls for help.
The President, of course, is making a bid to bring the conservatives back. He's going out of his way not to appear gleeful over the tax-increase victory. And he's calling conservative leaders to tell them that he understands their opposition to the bill - and that all is forgiven and forgotten as far as he is concerned.
From the President's own camp come expressions of triumph - although, again, guardedly uttered.
The Reagan people say that the public, despite some confusion over the tax issue, saw in the President's victory on the tax increase clear evidence that he is still very firmly in command.
According to a new Gallup poll the public's overall evaluation of the President has been practically deadlocked since early March, with about equal numbers of Americans approving and disapproving of the way Reagan is carrying out his duties.
Further, the President himself is said to feel that while the tax rise was prompted by his inability to gain all the spending cuts he asked for, he still is on track in his efforts to reduce the size of federal government and its spending.
One top aide put it this way: ''We feel that the President's counterrevolution is going right ahead. We hadn't counted on the recession and, hence, the huge deficit. But we really haven't lost any momentum in turning this country around.''
The Democratic perception of the President today cannot be easily capsulized.
Some Democrats contend openly that Reagan is on the ropes - that he has abandoned his supply-side approach to the economy and, in so doing, conceded a failure in planning for which the voters this fall will blame him.
They say the public finally is catching on to the President, that they are seeing through his captivating personality and finding only a man with oversimplified thinking and solutions. They say the honeymoon is over and that soon it will become apparent that Reagan has given the government his best shot - and that he is destined to be a one-term president.
But while these Democratic leaders may also be more critical of the Reagan administration these days, they continue to concede that the President remains politically formidable.