President Reagan's budget ax has swung toward the backyards of two of the Senate's most powerful figures, and they're fighting back like ordinary mortals.

In scraping together targets for Reagan's second round of spending reductions, the president's budget-cutters zeroed in on major water resource projects in the states of Tennessee and Louisiana -- the home preserves of Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) and Russell B. Long (D-La.), ranking member of the taxwriting Senate Finance Committee.

The cuts are not of the megabuck proportions of some of the items in Reagan's initial $41.4 million package of spending reductions unveiled last month, but they point up the political pain that is building up as the administration digs ever deeper for roughly $10 billion in additional budget sacrifices.

Both Baker and Long, who will be key players in the upcoming fight over Reagan's tax and spending proposals, are committed to the notion of a leaner federal budget, but both also have a keen sense of the limits of political self-sacrifice. So both have gone to bat -- in different ways and with different levels of success -- to keep what they can of their endangered projects.

Long's Louisiana appears to be the bigger loser so far.

At stake for Louisiana is $120 million that the Carter administration requested for fiscal 1982 to continue construction of the Red River navigation project, linking Shreveport to the Mississippi River.

At the instigation of Sen. J. Bennett Johnston (D-La.), Johnston, Long, two of the state's House members and Republican Gov. David Treen of Louisiana met yesterday with Reagan and his budget director, David A. Stockman, in an effort to keep the project going -- but to no avail, according to Long aides.

"There was no give," said one aide after the meeting. Although the project, for which $323 million already has been allocated, was not killed outright, Johnston said the delay may jeopardize the entire $1.6 billion endeavor. Johnston, strategically positioned as a member of the Appropriations and Budget committees, plans to continue the fight. Long, characteristically, held his cards close.

"No state or group of individuals should be singled out for more sacrifice than others if budget-cutting is to be fair and uniform," said Long, sounding not unlike some of the northeastern and midwestern Democrats who have been complaining about social program cuts.

Baker's source of concern is money to continue assembling and developing the Big South Fork National River and Recreation Area, an ongoing Corps of Engineers project for which the Carter administration recommended $26.9 million for fiscal 1982. It, too, was on an early hit-list for Reagan's second round of budget cuts, which included the Yatesville reservoir in Kentucky as well as the Red River project.

Baker put his staff to work negotiating with Stockman's Office of Management and Budget, and as of yesterday Baker aides said that about $10 million remained in the budget for the project, which straddles the Tennessee-Kentucky border in a scenic but coal-rich gorge region.

But Baker apparently has not given up on getting more for the park, including additional land as well as such improvements as access roads.

"I'm perfectly willing for us to take our cuts on this project . . . along with everybody else, and to stretch out time for completion of this new national park," Baker said yesterday. "But I oppose elimination of the request all together."

The majority leader said he is "reasonably optimistic" that he will prevail.