This is the week that Congress stops admiring its bouquets and starts poking around in the thorns.

It has set its stripped-down spending targets, reaping praise for ostensible self-discipline. Now, under renewed pressure from the Reagan administration, it will buckle down to the real work, the more painful work, of cutting programs to meet those targets.

In less than two weeks, under the terms of the first budget resolution for fical 1982 that Congress adopted last month, congressional committees are supposed to come up with more than $35 billion in program cuts.

In adopting the resolution shortly before recessing for Memorial Day, Congress gave each of its major authorizing committees, 14 in the Senate and 15 in the House, a lumpsum dollar quota for cuts, along with a June 12 deadline for making them.

It is up to the committees to draft the necessary legislation, which will then be assembled by the budget committees of the two Houses for enactment into law, theoretically by the middle of June.

There will be plenty of winching, and probably some flinching, as the committees, more experienced in adding to programs than subtracting from them, grope for ways to meet their targets or to wiggle out from under them.

To keep the flinching from getting out of hand, the Reagan administration intends to apply the same kind of pressure that it did in winning approval of the spending targets and cut-back instructions to committees.

The new campaign will start today with a news conference by Budget Director David A. Stockman that has been billed as a "seminar" on the pitfalls that may lie ahead in Congress.

But one man's pitfalls are another's opportunities, and House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) is openly encouraging Democrats to offer amendments on the House floor to block some of the cuts in social programs that Democrats have championed over the years.

"We should give the members of the Congress an opportunity to vote on the programs that made America great," O'Neill said in disclosing his strategy last month. Reasserting his intentions last Thursday, the speaker said: "If that means busting the budget, then I'm for busting the budget."

Reagan goes into the fight with the upper hand. Edspite problems with his proposals for tax cuts and reductions in Social Security benefits, he's had an almost perfect winning streak on the budget.

Moreover, not all Democrats are enthusiastic about O'Neill's strategy. House Budget Committee Chairman James R. Jones (D-Okla.), for one, is adamantly insisting on compliance with the targets, as least as far as overall savings are concerned.

But Reagan has yet to face this test of real cuts in real programs, submitted separately (if O'Neill has his way) from the protective cover of the overall Reagan austerity program. It is here that O'Neill figures the Democrats may have a chance for a comeback, or at least a chance to force the Republicans and their conservative Democratic allies to make some painful, embarrassing choices.

O'Neill has already staked out two major battlegrounds: loans for college students and the school-lunch program, which together account for about $2 billion of the proposed cuts.

There probably will be more in the way of salvage operations, especially from within the jurisdiction of the House Education and Labor Committee, whose chairman, Rep. Carl D. Perkins (D-Ky.), has said his allotted quota of more than $10 billion in cuts is too large to swallow.

Perkins has the biggest quota of all, followed closely by House Ways and Means, which has already approved $9.1 billion of its allotted $9.2 billion in savings by cutting, deeply in some cases, into old age, unemployment, health and welfare programs.

On the Senate side, the Finance Committee exceeded its $9.3 billion quota with $10.3 billion in cuts approved even before the budget was adopted.

But the sharply divided Senate Labor and Human Resources Committee, with a jurisdiction that is comparable to Perkins' on the House side, had to go begging to House-Senate budget conferees last month for a little more money in order to avoid an ideological standoff.

The problems are more acute in the Democratic-controlled House than they are in the Republican Senate. But, even in the House, Rep. Leon E. Panetta (D-Calif.) of the Budget Committee estimates that nine of the 15 committees that have to make cuts will do so without great difficulty.

In addition to Ways and Means, the committees with the most difficult tasks are Agriculture, Banking, Education and Labor, Energy and Commerce, and Public Works and Transportation, Panetta said.

What happens if a committee fails to meet its target?

By law, the budget committees can only package the cuts, not change them. But they can draft amendments to make up the difference for consideration on the floor of the two houses. The House Budget Committee has vowed to do this, and the Republican leadership of the Senate, including Budget Committee Chairman Pete V. Domenici (R-N.M.), has said it will permit no slippage.

In the case of Perkins and his committee, the House Budget Committee is urging that the full amount of the cuts be drafted, even if the committee feels compelled to disavow them.

Budget Committee members shudder at the idea of having to draft billions of dollars worth of cuts in complicated health, education and social service programs, although they say they will do so if necessary.

This is only the second year that Congress has called on its committees to make "reconciliation" cuts (so-called because they are aimed at reconciling spending with revenues and budget targets).

The reconciliation process was included in the 1974 Budget Control Act, largely as a tool for squeezing spending into availabe revenues when a second budget resolution with binding spending ceilings is adopted in the fall of each year. But it was not employed until last year when Congress, struggling in vain for a balanced budget, ordered cuts as part of its first budget resolution.

Even though the deficit reductions that were sought last year were much smaller $6.4 billion in spending cuts and $4.2 billion in extra revenues, Congress failed to meet its goal by a substantial amount.

After months of deliberation, rather than the few weeks contemplated this year, Congress finally approved $4.6 billion in spending cuts and $3.6 billion in additional revenues, for an overall total of $8.3 billion rather than $10.6 billion.

Of the projected spending cuts, nearly $1 of every $3 never got made. Moreover, critics complained that some of the cuts were cosmetic ones that would actually lead to more spending in future years.

So dazzling was the spectacle of congressional spending discipline of any kind, however, that few quibbled about the lapse last year. But a comparable amount of slippage this year, another $1 out of $3, would amount to about $10 billion in lost savings. It would be noticed.