The Senate late Thursday approved $475 million more in aid for Israel than President Reagan wants, and in the process dealt a potentially serious blow to the credibility of the administration's efforts to pressure Israel into agreeing to a timetable for withdrawing its troops from Lebanon.

The 57-to-41 vote on an $11.5 billion foreign aid package saw 29 Republicans turn aside strong administration objections and join with 28 Democrats to support the measure. Voting against were 24 Republicans and 17 Democrats.

There is still a strong possibility that the vote will be reversed. The amount approved by the Senate must be accepted by the House, which opted for a lower figure more in line with Reagan's wishes; even if that happens, the president is expected to veto the stopgap spending bill in which the Israeli aid money is included and thus force the Senate to consider the matter anew.

Nevertheless, administration sources conceded yesterday that the Senate's decision to defy Reagan's wishes at a time of strained U.S.-Israeli relations could have the psychological effect of convincing Israeli Prime Minister Menachem Begin that Reagan cannot count on congressional support if he takes a get-tough approach with Israel, and that Israel thus can ignore U.S. pressures with relative impunity.

However, sources within both the administration and Congress also stressed that the Senate's action, while acutely embarrassing to the White House, should not be taken as a gauge of how Congress is likely to react in future situations involving Israel.

Instead, most sources agreed, the Senate vote resulted primarily from a confluence of special factors including coincidences of timing, conflicts in the White House's legislative priorities and a misconceived, badly executed lobbying effort by the administration.

In particular, administration officials noted, the president, while concerned about the Israel aid issue, places an even higher priority on lobbying Congress to fund the MX missile and fighting a Democratic-sponsored jobs bill. For that reason, they said, it was not possible to oppose the aid vote as vigorously as would have been the case under other circumstances.

The timing of the Senate aid vote was especially embarrassing to the administration, coming as the White House was signaling impatience with what it regards as Israeli intransigence in the Lebanon talks and was making it known that special envoy Philip C. Habib had been instructed to take a tough line, if needed, to break the deadlock.

At issue is the Senate's approval of funding levels for foreign aid in the current fiscal year. The measure includes $2.6 billion for Israel, reflecting an increase of $125 million in economic aid and a transfer of $350 million from military loans to military grants.

The amendment carries over into a stopgap funding bill the same aid level for Israel voted earlier by the Appropriations Committee in a now-stalled foreign aid bill.

The drive to increase aid to Israel originated several months ago among senators anxious to make a gesture toward the Jewish state after the Senate refused to block the sale of airborne warning and control system (AWACS) planes to Saudi Arabia.

Initially, the administration argued that giving so much to Israel would take limited funds away from other deserving recipients.

However, although the administration was not asking for cuts below its requested level, many senators feared that a vote against the increase would look like a vote to reduce aid to Israel. The administration reinforced that impression earlier this month, when it charged that approving additional aid would give Arab governments the impression that the United States endorses Israel's continued occupation of Lebanon.

Supporters of the increase argued that the administration was being hypocritical, since it is an open secret that the White House is about to approve a substantial arms sale to Jordan, which so far has not responded favorably to Reagan's Mideast peace initiatives. King Hussein of Jordan is to confer with Reagan at the White House on Tuesday. Yesterday, 182 House members from both parties urged Reagan in a letter to reject any new arms sales to Jordan until Hussein becomes more cooperative. A similar Senate resolution has 52 sponsors.