WASHINGTON — In an election-year embarrassment for Republicans, Senate GOP leaders have put off action on the annual budget blueprint.

Budget Committee Chairman Mike Enzi, Republican of Wyoming, announced the delay on Monday, which came as the House is gridlocked on its own plan. Several dozen House conservatives are opposing a draft companion measure because it endorses spending increases for domestic agencies that were part of last year’s bipartisan budget and debt pact.

The combined developments are a predicament for Republicans, who were quick to criticize Democrats for failing to produce budget plans when they controlled the House and Senate. The delay does spare the party from a divisive debate conducted against the backdrop of a heated presidential race.

Republican hopes of moving quickly on legislation this year and boost the prospects of a half dozen vulnerable incumbents have hit a roadblock. An energy bill is on hold, tied up in a separate dispute over federal aid to Flint, Mich. Criminal justice reform is falling victim to election-year politics.

An exception is legislation on track to pass the Senate this week on combatting heroin and opioid abuse.

A bitter battle over filling Supreme Court vacancy created by the death of Justice Antonin Scalia last month is also consuming the Senate, with Republicans vowing to block any nominee of President Obama.

Instead, top Senate leaders of both parties pledged on Monday to try to work together to advance an upcoming round of agency budget bills in hopes of getting the annual appropriations process back on track and avoid a catchall omnibus spending bill at the end of the year.

Enzi said he will keep working toward a plan, but noted that the annual spending bills can go forward under last year’s budget deal.

‘‘The Senate Budget Committee will continue to discuss the budget as well as improvements to the budget process that would increase fiscal honesty, stability in government operations and the ability to help govern our nation,’’ Enzi said.

The budget panel is stocked with Republicans facing difficult reelection races, including Kelly Ayotte, Republican of New Hampshire, Rob Portman, Republican of Ohio, and Ron Johnson, Republican of Wisconsin.

This year’s worsening fiscal picture means that meeting the GOP goal of balancing the budget would require even deeper spending cuts than the $5 trillion-plus over 10 years proposed in last year’s budget.

The annual budget resolution is a nonbinding blueprint that sets goals for follow-up legislation. While it sets parameters, it doesn’t increase spending or impose cuts by itself.

The budget sets a limit for the annual appropriations bills, and, in some years, is used to set in motion special tax or budget legislation that can’t be filibustered in the Senate.

Senate Democratic leaders weighed in Monday as well in a letter to Senate majority leader Mitch McConnell, Republican of Kentucky, promising to help move the annual appropriations bills through the chamber.

They said top Republicans should make sure key domestic programs are adequately funded and that the measures are kept clean of GOP policy ‘‘riders.’’