Prince George's County officials said yesterday that County Executive Lawrence J. Hogan's political feud with four local state senators had saddled the county with what its budget director called "a $4.5 million problem."

Because the four senators succeeded in blocking a measure that would have removed a technical obstacle to the county's authority to issue bonds. Prince George's almost certainly cannot borrow money for at least a year.

As a result, the county will have to dip into its already-tight 1980 operating budget or use most of its existing surplus to pay about $4.5 million it owes for the construction of some hospital projects and a fire station.

The county's inability to issue bonds also means that it will lose $14 million in state funds that would have financed eight school construction projects. The state aid is contingent on the county's willingness to put up $1.8 million of its own money.

Furthermore, road improvements, new street lights, and other construction projects that had been planned for 1980 now will almost certainly be canceled for at least a year, county officials said.

County Council members, while calling the bond problem "critical" and "disastrous," yesterday conceded that it was the result of a tangled political confrontation that began when Hogan, a Republican, offended the Democratic senators, and worsened when members of the all-Democratic council hesitated to intervene on Hogan's side.

"I never imagined that this [bill] would really bog down when it came down to the practicalities," said one council member, Sue V. Mills, who was clearly shocked by the county's predicament.

"We screwed up," said another council member, "We didn't panic until it was too late."

The bill at issue was a measure designed to eliminate conflicting language in the county's charter that resulted from the voter's passage of the revenue-limiting TRIM charter amendment last fall.

Technically, the county must back its bonds with "unlimited taxing power." TRIM, which limits tax revenues, therefore prevents the county from issuing bonds to borrow money.

The bill seemed assured of passage until Hogan cut out of his 1980 capital budget the funding for a library in the home district of one of the senators, B.W. (Mike) Donovan.

Donovan approached Hogan and asked for a "compromise." He would vote for the bill, he said, if Hogan restored part of the funds for the library.

When Hogan refused and dispatched a sharp letter to the senators accusing them of attempting to hold the bill "hostage," Donovan and Senators Arthur Dorman, Peter Bozick and John J. Garrity decided, council members said yesterday, that it was time to teach the new Republican executive a lesson.

However, Bozik, Garrity and Dorman said that they opposed the bill-which would have authorized the county to create a special fund to back its bonds-because it would permit Prince George's to spend an unlimited amount of tax dollors on capital projects, thus violating the intent of the TRIM amendment.

The trio also accused Hogan of trying to circumvent TRIM after vigorously supporting it during his campaign.

And, finally, "I don't believe that the projects [in the capital budget] are all that earth-shattering," Bozick said. "No starting date was given as to when they would be [finished]. . . It looked like a hit parade list [of projects] from everybody's districts."

"The attitude of the senators was that since Hogan had gone around campaigning so much for TRIM during the election, then, he could just live with it now," said one council member yesterday.

Despite the bitterness between the senators and Hogan, the dispute might have been resolved and the bill passed, council members conceded yesterday, had it not been for their own ambivalence on the issue.

Council member Parrris N. Glendening, for example, said that as late as last Thursday he told Bozick that the senators would not cause the county major problems if they blocked the bond bill. Bozick said yesterday that council chairman William B. Amonett also made similar assurances.

Glendening and other council members reversed themselves and sent emmisaries to lobby hard for the bill in the final days of the session. But by then it was too late. "The bill had simply got involved in a political process that didn't really have anything to do with the bill itself," said Royal Hart, the council's legislative liaison. "And try as we might, we simply couldn't blast it loose."