By David Morgan and Katharine Jackson

WASHINGTON (Reuters) - The Republican-controlled U.S. House of Representatives began debating the first of 12 fiscal 2024 spending bills on Wednesday, as lawmakers edged toward a looming showdown with the Democratic-led Senate that could trigger a government shutdown this autumn.

The House voted 217-206, roughly along party lines, to adopt a measure that opened debate on a military construction and veterans affairs appropriations bill, amid signs that Republican leaders were near an agreement with hardline conservatives who have demanded cuts that would leave next year's overall spending at a fiscal 2022 level of $1.47 trillion.

Hardline conservatives, including members of the House Freedom Caucus, warned Republican leaders this week that they would not support appropriations bills without assurances on spending.

Freedom Caucus member Andy Ogles told Reuters that the two sides were trying to finalize such a deal.

"It's a work in progress. Nothing's finalized. But I'm cautiously optimistic," Ogles said without providing details.

"Part of that process is how do you get assurances that will actually achieve that number," the Republican added.

McCarthy's office was not immediately available for comment.

The House is expected to vote on passage of the military construction bill later this week and could turn as early as Thursday to a second appropriations bill, which would fund agriculture programs, rural development initiatives and the Food and Drug Administration.

The agriculture bill could face resistance from more moderate Republican lawmakers, including some who oppose its restrictions on abortion services.

Representative Don Bacon said the legislation could also lose support from the center if last-minute changes led to further cuts in spending. "If these guys keep pushing for more cuts, it may be in jeopardy," the Republican said.

House Speaker Kevin McCarthy and other Republican leaders hope this week's votes will give them the upper hand against the Democratic-led Senate. Each chamber is expected to pass its own spending legislation and then try to hammer out compromise bills that can be sent to Democratic President Joe Biden.

Lawmakers have until the current fiscal year expires on Sept. 30 to fund the government or risk a partial government shutdown.

But with hardliners pushing for lower spending, the House and Senate are at least $120 billion apart, with Senate appropriators aiming at the $1.59 trillion in fiscal 2024 discretionary spending agreed by McCarthy and Biden in June.

House Majority Leader Steve Scalise said negotiations between the two chambers could begin during the annual August recess in an effort to move them toward agreement in September.

Biden on Monday vowed to veto the House Republican spending bills if they make it to his desk, saying they backed away from the deal.

The military and veterans bill would provide $155.7 billion in discretionary spending for military construction and veterans affairs. The health and agriculture bill would provide $25.3 billion, but that includes about $7.5 billion moved from Democratic programs.

Democrats rejected the military construction bill, saying it would slash important programs and impose "a kitchen sink of culture wars" on the military and veterans.

"It would prohibit training that helps people from different backgrounds work together, that addresses the inequalities that still exist in our military. It would allow homophobia to run rampant," said Democratic Representative Teresa Leger Fernandez.