After rejecting fat budgets, skinny budgets and some in-between, the House today faces a choice between more traditionally shaped Democratic and Republican spending plans, along with the real possibility of no budget at all.

So nervous were party leaders yesterday about the fate of the two party-drafted choices, featuring a $100 billion-plus deficit from the Democrats and deep social program cuts from the Republicans, that they were already talking privately about a fall-back compromise in case of failure.

President Reagan reached back from Europe to put his arms around the Republican plan, describing it as "the best available alternative," and it was considered to have a better chance of passage than the Democratic plan.

But many lawmakers questioned whether even it would pass, and some said if it did not, there might be no budget for the fiscal year that starts Oct. 1, especially if today's debate intensifies partisan hostilities.

Speaking of the choice before the House today, House Minority Whip Trent Lott (R-Miss.) summed up the view of the leadership of both parties: "It may not be pretty but the alternatives are horrendous," including "chaos and confrontation" in Washington and a "pox on everybody" message from the voters back home.

Others were even more explicit in their pessimism.

Without the discipline of a budget resolution, setting targets for spending cuts and tax increases, and requiring legislative committees to meet the targets, the fiscal 1983 deficit could hit $200 billion, warned House Budget Committee member Leon E. Panetta (D-Calif.).

And, without a signal of fiscal restraint from Congress, both the Federal Reserve and the financial markets are likely to tighten up in such a way as to choke off economic recovery, warned Rep. Ralph Regula (R-Ohio), another Budget Committee member.

What if the House, which rejected eight different budget alternatives two weeks ago, stays in its negative mood today and rejects the Democratic and Republican plans, along with Reagan's original budget, which is being used as the vehicle for consideration of the party-sponsored alternatives?

Many members believe there will be yet another attempt at compromise, and House Speaker Thomas P. O'Neill Jr. (D-Mass.) indicated he would meet with other House leaders before the week's end to try to come up with something to get the budget to a conference with the Senate, which has passed its version of the budget.

But Republicans discounted any fall-back plans, warning that such talk could jeopardize passage of any budget today. And there was no sign that a bipartisan budget compromise, which has eluded congressional leaders for nearly six months, might succeed now.

Time is getting critical because Congress must act within the next two or three weeks to extend the debt ceiling. The government cannot continue to operate long after July 1 without more borrowing authority, and some members of both houses are balking at raising the ceiling without some assurance that deficits will start coming down.

Beyond the debt measure are the appropriations bills that are needed to operate the government after Oct. 1. Without a new budget, Congress would have to waive existing budget ceilings for money bills, which could be politically touchy in an election year. Moreover, Reagan could threaten to veto any bill that exceeds his spending target, setting the stage for repeated veto confrontations with Congress.

Almost by default, Congress would probably then turn to omnibus stopgap funding bills, called "continuing resolutions," which are getting to be a habit on Capitol Hill anyway. With continuing resolutions as well as regular appropriations bills, Reagan would be well-positioned to rule by veto, in the opinion of some Democrats, who are clearly unhappy at the prospect.

But this is not to say that Reagan would necessarily win from a budget stalemate, according to Republicans.

Without a budget, it will be even more difficult than it would be with one to pass tax increases or to cut benefit entitlement programs that are funded without regard to annual appropriations, they say. This would mean higher deficits--higher "Reagan deficits," they note.

Moreover, "We'll be blamed . . . because most Americans want a budget and they think we're in control of the government," lamented a House GOP leadership aide. Reagan could continue to blame House Democratic leaders for budget paralysis, but many Democrats could campaign more easily in the fall without complicity in any of Reagan's economic program.

Even if the House approves a budget, today or sometime later, there is no certainty of the lower deficits that Congress is pursuing, as if in quest for the Holy Grail.

Both Democratic and Republican plans call for "reconciliation," under which legislative committees are ordered to raise taxes and cut spending to meet the budget targets. They also would prevent final passage of any money bills that exceed the spending targets, at least until final budget ceilings are approved, presumably this fall.

Congress met the reconciliation targets for about $35 billion in spending cuts last year, but Reagan's hold over Congress was considerably stronger then. Moreover, this year's spending cuts are coupled with tax increases amounting to $20 billion for the Republicans and $31.7 billion for the Democrats.

And, if it was this hard to adopt a budget, which does nothing more than set targets, just wait until Congress tries to pass the legislation to raise taxes or cut popular spending programs, some members are saying.