The battle of the budget, which will be played out on the House floor this week, has strained political relationships in both parties.

Democratic liberals, who have seen their programs cut, threaten to jump ship and vote against the budget if more cuts are made when the House votes on the preliminary resolution for the fiscal 1980 budget.

Democratic conservatives and younger members, fearful that the public pressure to cut spending could cost them their seats, want tohe budget cut more.

Both sides are unhappy with the budget as the Budget Committee has reported it out, calling for outlays of $532 billion and a deficit of $24.9 billion.

Last week, the Senate approved a budget resolution calling for $532.6 billion in spending, a $29 billion deficit and few changes from the fiscal blueprint President Carter offered in January. The House deficit figure is lower in part because of differing economic assumptions.

The normally united Republicans are having their own problems this year as they compete among each other to offer budget cuts. "This year we just don't have our act together," a Republican leadership aide said.

Hard-charging freshman Republicans, filled with Proposition 13 fervor, want to support a balanced budget amendment, tough it is unlikely to pass.

The Republican leadership is offering amendments that would cut the deficit to about $15 billion and provide for about a $12 billion tax cut in fiscal 1980, though that too is likely to fail.

And finally, Rep. Marjorie Holt (R-Md.), who has been the Republican leader on budget cuts in past years, is offering an amendment with Rep. Ralph Regula (R-Ohio). Holt is somewhat miffed that the Republican leaders waited so long to propose their own amendment and aren't supporting hers. Her amendment would put the deficit at about $19 billion and would restore some revenue sharing for states. That would put the budget about in line with what the Senate has already passed.

Her amendment may pass, but if it does, liberals will probably vote against the budget resolution. AFL-CIO chief lobbyist Ken Young said, "If Holt-Regula passes, we will be urging members to oppose the budget resolution."

That may not matter if the amendment encourages Republicans to support the budget resolution, but it is not at all clear whether they will. "That's the $64 million question," Budget Committee Chairman Robert Ciaimo (D-Conn.) said.

House Republicans traditionally have opposed the budget resolution on principle, arguing that the deficits are too high.

That has forced the Democratic leaders into delicate negotiations with conservatives and liberals of their own party. No one is sure whether such negotiations will work this year.

Giaimo will accept a $250 million increase in money for veterans. And a package by Rep. Paul Simon (D-Ill.) that adds money for two destroyers Iran ordered and canceled plus increases for food stamps. Small Business Administration disaster loans and countercyclical aid for cities will also be accepted in the hopes that it will attract hawkish conservatives and blacks and big-city liberals.

But it will not alleviate the political pressure for cuts. And that pressure is making the old budget coalition of conservative Democrats and liberals come unglued.

The Congressional Black Caucus already has voted unanimously to oppose the budget resolution as it is now, reasoning that no matter what happens things can't get much worse for blacks and believing there's nothing to gain mediating a fight among middle-class whites.

Rban and lbor groups feel almost the same way.

But Giaimo says that if the budget resolution is defeated and the Budget Committee has to go back and try again, it is only likely to come back with a lower figure, not a higher one.

Just to confuse things further, one influential liberal Democrat, Wisconsin Rep. David Obey, will offer his own version of a balanced budget. Obey is one of tose liberals angry at what he considers the posturing of conservatives and younger Democrats.

"I really get a kick out of how the bleeding heart balanced budgeters want more money for veterans and Iranian ships," Obey said. "I hope those people will put their votes where their mouths have been and face the consequences of their own rhetoric," by voting for his amendment.

"If other people are going to play games, I'm going to play games too," Obey said.