WASHINGTON, June 16 (Reuters) - Democratic leaders in the House of Representatives hope to push through legislation by July to impose stricter limits on tax cuts and spending programs to avoid adding more red ink to the already bloated U.S. deficit, Majority Leader Steny Hoyer said on Tuesday.

President Barack Obama has been under pressure to bring burgeoning U.S. spending under control and last week urged the Democratic-controlled Congress to agree that any new tax cuts or automatic spending programs would not add to the deficit.

The effort comes as Congressional Budget Office estimated on Tuesday that the deficit will hit $1.825 trillion in fiscal 2009, which ends Sept. 30, and will be over $1.4 trillion in fiscal 2010, furthering pressure to stop adding more red ink.

"This is only one component, obviously, of the way back to fiscal balance which we must do," Hoyer told Reuters in a telephone interview, adding that Democratic leaders will unveil the bill on Wednesday and want to pass it by next month.

To address concerns in the Senate that the legislation does not address expanding existing programs, Hoyer said he planned to meet with a leading skeptic, Senate Budget Committee Chairman Kent Conrad, to discuss the legislation.

"What I'm going to try to convince Senator Conrad of is that this a very positive step forward," Hoyer said while acknowledging that Conrad would like to go further where all programs, old and new, are on the table.

"What I will tell him is if he can send me bills that are paid for ... then we'll certainly fight to pay for them" in the House, Hoyer said.

Republicans have warned that programs such as a proposed health care reform plan by Democrats would add to the deficit for years and have also criticized the $787 billion economic stimulus program that Congress passed in February. (Reporting by Jeremy Pelofsky, editing by Jackie Frank)