House Democrats, eager to avoid appearing "Reaganized" but fearful of being tagged as big spenders, agreed yesterday to push for a limited extension of supplemental jobless benefits for the long-term unemployed.

Faced with imminent expiration of the program, they agreed in a caucus to attempt to pass legislation next week to extend benefits for three months for those currently on the rolls and perhaps for at least some of those who qualify after March 31.

Senate Republicans appeared likely to act only if the House measure is within range of satisfying President Reagan, who has said he opposes extending the program.

Senate Majority Leader Robert J. Dole (R-Kan.) indicated reluctance to bring up such a measure unless it is a "scaled-down version" of the present program and will not encounter presidential opposition.

Under the program, about 325,000 unemployed workers are getting up to 14 weeks of benefits after exhausting their regular 26 weeks of assistance. The program expires on Monday, and final benefits will be paid the week of April 7.

With unemployment still in double-digit rates in some areas, pressure is strong in Congress for extension of the supplemental benefits program. But Reagan said last week that he opposes extending the program as long as the economy is expanding and creating jobs.

Despite earlier talk of an 18-month extension that could cost $3 billion, House Democrats settled yesterday for a stopgap measure that would cost less than $300 million.

As explained by Rep. James L. Oberstar (D-Minn.), a leading backer of extension, the measure will be put on a fast track for House action by next Thursday, the day before Congress is to leave for its week-long Easter recess.

In the meantime, Congress would go to work on a long-term overhaul of the program that Oberstar said could include limiting assistance to areas and periods of high unemployment.

Vowing that Democrats will not "allow this party to be Reaganized," Oberstar said the Democrats are determined to move on the issue, even over the president's objections.

A House Ways and Means subcommittee is expected to meet today to begin drafting the legislation, but no action has been scheduled in the Senate, where a bipartisan group of "Rust Belt" senators is pushing a $1 billion measure to extend the current program for six months.

However, an aide to Senate Finance Commitee Chairman Bob Packwood (R-Ore.) said that, depending on what is done by the Ways and Means subcommittee, the Finance Committee may consider a version of the legislation next week.

A stripped-down version that would continue benefits only for those now on the rolls would be "a basis to start from," the aide said