As if there was not enough riding on congressional passage of the budget summit agreement, Sen. Tom Harkin (D-Iowa) and members of the Appropriations subcommittee he chairs are hoping it will rescue them from a senatorial turf fight that they seem likely to lose.

The controversy is with the Senate Finance Committee, whose chairman is Sen. Lloyd Bentsen (D-Tex.). Harkin, who is up for reelection in November, heads the labor, health and education subcommittee. His most powerful potential ally is Sen. Robert C. Byrd (D-W.Va.), chairman of the Senate Appropriations Committee and a fierce defender of the panel's turf and prerogatives.

So far, however, Byrd appears inclined to support Bentsen, whose support he needs to pass a budget summit agreement that protects the Appropriations committees from feared deeper cuts. Byrd reportedly has told Harkin to work out his problem with Bentsen before bringing the $173.4 billion bill to the full Appropriations Committee.

Bentsen insists that Harkin's bill contains three legislative provisions that are under his committee's jurisdiction and should not be included in an appropriations bill. Together, they raise $245 million in new revenue and savings that Harkin proposes to apply to accounts in his bill that are seriously underfunded.

With Bentsen unwilling to give ground, Senate appropriators are looking to the summit agreement to provide a face-saver. The budget deal could give Byrd some additional funds to allocate. There might be just enough for the labor, health and education subcommittee to enable Harkin to finance his bill without resorting to the objectionable provisions.

The three disputed provisions would cap the annual growth in the administrative costs of the foster-care program by 10 percent, tighten state eligibility for a special federal incentive payment for enforcing child support and force private insurers to pay their share of health coverage before Medicaid kicks in.

A fourth provision, to which the Finance Committee reportedly does not object, would charge nursing homes and other health facilities a fee to cover the administrative costs of certifying them to receive Medicare and Medicaid benefits.

Harkin's travails began earlier when the full Appropriations Committee allocated his panel $800 million less in outlays than the counterpart House subcommittee. Since then, he has been scrambling to satisfy a myriad of causes and using every fiscal maneuver to do so.

The subcommittee bill increases funding over 1990 for compensatory education by $1 billion, and funnels extra funds to Alzheimer research, but hundreds of other causes received only small increases, or got no money at all. For example, a group of Senate appropriators led by Sen. Brock Adams (D-Wash.) have vowed to add money in 1991 for the AIDS-care bill signed by President Bush in August but not funded in Harkin's bill.

In the background is election politics. Some Harkin critics charge that he rearranged priorities in the spending bill to help him with politically potent Iowa constituencies, such as the elderly, while shortchanging those with low impact at home, such as the AIDS community.

The cap on the federal contribution to the foster-care program would put a brake on one of the fastest growing federal programs, and has been attacked by the American Public Welfare Association. But it may not hurt him in Iowa, where people are concerned about the runaway federal deficit, sources said.

Iowa, it happens, is also one of the handful of states that will continue to be eligible for the special incentive payment for enforcing child-support judgments under the new, tighter formula proposed by Harkin's subcommittee.