The House is expected to hand President Carter another legislative setback today when it votes a public works money bill for fiscal 1978 that contains funds for water projects he wants halted.

A Carter-backed effort to delete funds for 17 presidential "hit list" projects and bar money for 12 more he doesn't want started is expected to fail, according to House Democratic leaders.

Yesterday, in an attempt to head off still another Carter congressional defeat, Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) and other members of the House leadership met with Health, Education and Welfare Secretary Joseph A. Califano Jr. in an effort to work out differences on the Labor-HEW money bill is that is scheduled to come up for a House vote Wednesday.

As sent to the floor, the measure is $1.4 billion above Carter's recommendation For Califano's agency.

After a session yesterday morning with the President, the HEW Secretary met with O'Neill and asked for cuts in two programs - impact aid for schools and the student loan program.

In his budget recommendations, Carter asked that both programs be halted. Instead, the House Appropriations Committee added more than $700 million to continue both.

According to O'Neill House lead-encountered by suggesting to Califoornia that "we leave the (Labor-HEW) budget where it is" and that any floor amendments be opposed. In return, O'Neil wanted assurances the White House could not offer its own budget-cutting amendments and would not support a move by House Republican Whip Robert H. Michel (III) to cut $560 million from the measure.

Neither the House leaders nor Califano would indicate yesterday evening what had been agreed upon. "Negotiations are continuing," a spokesman for the HEW Secretary said.

Hanging over both money bills is the threat of a presidential veto. O'Neill and other Democrats want to avoid that situation, particularly on the Labor-HEW bill, which supports the broad social programs favored and designed by the Democratic Party.

The votes on the Carter-backed cuts to the public works bill could provide a clue on how a veto of the measure would fare. "If the pro-Carter side drals 150 votes or more, it would be an indiction that the House could not muster the two-thirds vote needed to override a veto.

The President's water-project fight is being led by a liberal Republican, Rep. Silvio O. Conte (Mass.) and a Southern Democrat, Rep. Butler C. Derrick (S.C.). Derrick has become a political folk hero at the White House for supporting the President's effort to end the $254.9 million Richard Russell Dam project in his district.

Until last week, according to supporters of the Conte-Derrick amendment, the White House wasn't much help. Then, however, the President's men weighed in, producing personal, pep-talk letters from Carter to a variety of members who are hoped to vote for the cut. But as of the weekend, Carter was not taking a direct part in the lobbying effort.

Majority Leadrer Jim Wright (D-Tex.) and Rep. Tom Bevill (D-Ala.) chairman of the House Appropriations subcommittee that ignored the President's water project "hit list," are leading the forces against the White House amendment.

A Home aide working for the Wright side said Friday that the entire House Democratic leadership is "supporting the committee down the line," and said so at last week's committee policy meeting.

However, a spokesman for O'Neill said the Speaker "expects Bevill will win but has not expressed himself" on how he will vote.

O'Neill wants to avoid a vote here, also. He is in touch with Senate leaders who feel the same way. They are trying to cut an additional nine "hitlist" projects from the Senate bill so a House-Senate conference may end up eliminating more than one.

The theory is that if the House vote today shows that a veto override is impossible, O'Neill in the long run will be in better shape to get a few more "hit-list" project cut out and so convince Carter the "compromise" measure should not be vetoed.