The Senate yesterday brushed aside Democratic proposals to roll back some of President Reagan's budget and tax cuts, as the leadership sought to keep these and other political blandishments from bogging down a debt-ceiling increase that Congress must pass by Thursday.

Voting 58 to 30, the Senate rejected a proposal from Sen. Gary Hart (D-Colo.) to restore a cut Congress previously made in the school lunch program and instead reduce tax deductions for business meals and entertainment.

Then, by an even bigger margin of 74 to 13, it spurned another Hart proposal to defer the three-year, across-the-board personal tax cut until the federal budget is balanced.

The outcome was never in doubt. But the effort gave Hart and some other Democrats another chance to force Republicans into votes that might prove to be politically embarrassing in the future -- although many Democrats refused to join in the exercise, especially on the tax cut issue.

Senate jockeying over the debt bill came as House-Senate conferees made slow progress in resolving differences over a stop-gap funding resolution for the government, which is also due by midnight Wednesday, and as Reagan borrowed a new slogan for his campaign for still more budget cuts.

Appearing at a Republican fund-raiser in New Orleans, Reagan took note of congressional approval of his tax and budget cuts last summer and added: "We had a great victory with the passage of that budget and that tax bill. And yet I think we should remember a Japanese proverb: 'After a victory, tighten your helmet strap.' "

In the Senate, Hart's proposals were offered as riders to administration-requested legislation raising the national debt limit to just over $1 trillion. The current debt ceiling of $985 billion expires Sept. 30, and the administration is seeking the new ceiling to carry the government through September 1982.

Without a new debt ceiling, the government would lose its power to borrow money and thus to continue normal operations. Although Congress goes through jittery debt ceiling showdowns once or twice every year, this one is different because of the symbolism of a trillion-dollar debt, making it exceedingly painful for some lawmakers to stomach.

Even though Republicans control the Senate, the Reagan administration is taking no chance there. Reagan called a half-dozen or more GOP senators to nail down their support, and Vice President Bush is expected to make a rare appearance as presiding officer of the Senate (and potential tie-breaker) when the legislation comes up for a final vote tonight.

Last night Sen. William Proxmire (D-Wis.) took the Senate floor and vowed to hold it all night to dramatize the significance of a trillion-dollar debt, although he said he would not attempt to hold up passage of the bill today.

Senate leadership sources claimed enough votes to pass the measure, but probably only with some Democratic help. On an earlier debt-increase vote this year, Democrats withheld support until Republicans coughed up enough votes to assure passage.

The Senate's problems are heightened by the fact that any amendments would force the measure to be sent back to the House. The House passed the debt-ceiling increase, hidden away in its budget resolution, last summer. There is some doubt about whether it would do so again, in broad daylight, without many amendments and possible delay that could threaten continued government operations after Thursday. "It's a risk that I'd prefer not to take," said Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) yesterday in emphasizing Republican leadership strategy to fend off all amendments in the Senate.

In yesterday's debate, Hart claimed that Congress could raise $500 million in 1982 and $1.2 billion in 1983 -- enough to avoid spending cuts for school lunches -- by permitting deductions of only 70 percent of the cost of expense-account meals and entertainment.

"Congress has enough courage to take lunches away from schoolchildren," Hart contended, "but not enough to take them away from businessmen who eat at fancy restaurants and private clubs." Sen. Robert J. Dole (R-Kan.) said he couldn't "say the amendment is without merit," but added that it was "another attempt to avoid spending cuts" and criticized Hart's rhetoric as aimed at "media consumption."

Still pending was a proposal by Sen. William L. Armstrong (R-Colo.) to make it easier for a president to get congressional approval when he wants to rescind, or withdraw appropriations. Now both Houses must approve a recision. Armstrong would allow a recision to stand unless both Houses veto it.