President Obama’s budget suffered its latest ignominious defeat when the Senate rejected it on a 98-1 vote Tuesday evening, capping off the first votes of the budget season.

Democrats objected, saying the plan wasn’t really Mr. Obama’s, but Republicans said it had all the same numbers as the president’s blueprint, and so the vote counts as a rejection of his fiscal year 2016 plan.

“This is the president’s proposed budget,” said Sen. John Cornyn, the Texas Republican who forced the vote by offering the amendment, complete with the tax hikes, spending increases and deficit targets Mr. Obama had projected in the document he sent to Congress last month.

Rejecting presidential budgets has become standard in recent years. The Senate defeated Mr. Obama’s fiscal year 2011 plan by a 97-0 vote and his 2012 plan by a 99-0 vote.

Sen. Bernard Sanders, Vermont independent and Democrats’ point man on the budget, said the plan Mr. Cornyn offered didn’t include a minimum wage increase or some of Mr. Obama’s other policy prescriptions, so it wasn’t a legitimate representation of his budget.

“It is not what President Obama presented to the American people,” Mr. Sanders said.

But that argument was undercut somewhat by Sen. Thomas R. Carper, Delaware Democrat, who was the lone senator to vote for the Cornyn amendment Tuesday, signaling that at least one Democrat backed Mr. Obama.

Both the House and Senate are debating budgets this week. The documents aren’t binding but provide an outline of the legislative agenda for the rest of the year and, at least in the Senate, provide an opportunity for a freewheeling debate.

Any senator is allowed to insist on a vote on an amendment, forcing lawmakers to have to cast some politically dangerous votes.

Republicans are fighting each other over whether spending cuts should take precedence over enhanced Pentagon funding, while Democrats object to the GOP deals on several accounts.

Both the House and Senate GOP plans reach balance at the end of a decade through fierce spending cuts. Mr. Obama’s plan boosts spending and raises taxes, but still projects red ink for the foreseeable future.

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