President Reagan's budget lobbying blitz took its toll yesterday as Reagan nailed down the support of several wavering Republican lawmakers and a House Democratic leader conceded there is little the Democrats can do to outbid the president in the favors game.

Asserting that the White House has declared "open season" by courting members with invitations to state dinners and other goodies, Majority Whip Thomas S. Foley (D-Wash.) said the days of arm-twisting are over and Democratic leaders would be "roundly criticized " if they "even hinted " at passing out legislatiave favors.

"There aren't two White Houses . . . there aren't two sources of White House invitations," he lamented. An invitation to "have lunch with the speaker or sit in the speaker's gallery" just isn't in the same league, he observed.

But, as the House moved laconically through its second day of debate on Reagan's budget and a proposed Democratic alternative, Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) continued to insist that the tide had turned, contending that the White House lobbying campaign indicated that the president's program is sliding downhill. "We've got them on the ropes," declared O'Neill, who all but conceded defeat earlier this week.

O'Neill said his mail is now running 50-50 on the budget, after leaning overwhelmingly in favor of Reagan not long ago. "The American people, despite his character and charisma and wonderful ability at the microphone, are suddenly beginning to realize" the extent of the president's proposed budget cuts, the speaker said.

House Majority Leader Jim Wright (D-Tex.) also plunged into the fray, accusing the president of resorting to "fallacious and misleading" arguments in implying to wavering lawmakers that they can vote for his austerity budget and then fight later for their favored programs. "You can't have it both ways," contended Wright.

He noted that the Reagan budget, as revised with the president's blessing by Reps Phil Gramm (D-Tex.) and Delbert Latta (R-Ohio), includes billions of dollars worth of mandatory program cuts, including $11 billion from education and labor programs. "I don't know how he's going to fix that up," said Wright. "These are cuts, not targets."

The Gramm-Latta budget mandates cuts of about $38 billion through instructions to legislative committees to cut programs by that amount. The Democratic alternative drafted by the House Budget Committee mandates only $15.8 billion in program cuts but also calls for additional appropriations cuts of $23.6 billion.

Democrats are hammering at the severity of the mandated cuts in the Gramm-Latta budget in an attempt to pull wavering legislators to their side. Conversely, Republicans are using the difference to claim that the Gramm-Latta budget is the only one that assures real spending cuts.

Meanwhile, the Congressional Budget Office reestimated the two budgets under economic assumptions used by the Budget Committee and concluded that Gramm-Latta would spend $710.05 billion, compared with $713.65 billion for the committee version -- a difference of $3.6 billion.

In reference to Reagan's claim in a speech to a joint session of Congress last Tuesday that his budget would save $141 billion more than the Budget Committee's over three years, CBO concluded that only $300 million of the disparity was attributable to policy differences. Most of the rest was attributable to differences in economic assumptions, spendout rates and unspecified future savings, it indicated.

Among Republicans who went to the White House yesterday for budget chats with Reagan, at least three -- Reps. Guy V. Molinari and Gregory W. Carman of New York and Thomas J. Tauke of Iowa -- said they will vote for Reagan's budget despite some problems with specific cuts, according to the Associated Press. A fourth, Rep. Claudine Schneider (R-R.I.), was noncommittal, according to the AP.