Top Senate Democrat Harry Reid said though he was "disappointed we haven't been able to get something done", talks would continue later on Thursday.
Without a deal parts of the government will shut down at midnight on Friday.
"I do believe that all of us believe we can get to an agreement, but we're not there yet," Mr Boehner said.
US President Barack Obama met Mr Boehner and Mr Reid at the White House on Thursday afternoon for negotiations on a bill to fund the US government through the end of the fiscal year.
Mr Reid said talks would resume at 1500 local time (1900GMT).
The Democrats have accepted cuts of more than $33bn (£20bn) but some Republicans want cuts of more than $60bn to tackle the US's huge deficit.
'Non-essential services' The US government has subsisted without a long-term budget since 1 October, funded by a series of temporary measures.
The most recent of those is set to expire at midnight on Friday, forcing all government services deemed non-essential to shut down and keeping hundreds of thousands of government workers at home.
- US government shut down 10 times during the Carter and Reagan administrations
- Last shutdown was in 1995 under President Bill Clinton
- Law passed in 1870 prohibits government from operating if a budget hasn't been passed
- This is interpreted to exempt so-called essential services
- These include: National security, air traffic control, some but not all medical services
- But not: Processing of visas and passports, museums and monuments, answering work emails (by non-essential workers)
Republicans in the House approved another temporary measure on Thursday - but one that would cut $12bn from spending in a single week.Mr Obama said in a that the US government could not continue to operate on a week-to-week basis and that he would veto the Republican bill if it arrived on his desk.
Following the negotiations on Thursday, Mr Boehner said he expressed his direct disappointment to the president over his intentions to reject the measure.
Senate Democrats, who must pass the bill before it goes to Mr Obama, have also said they will reject it.
Democrats have said Congress has already passed too many temporary bills and must work towards a measure that will fund the government until 30 September, the end of the budget year.
On the wider spending proposals, Republicans, urged on by the Tea Party movement, are calling for a far greater reduction in the government budget than Democrats are willing to concede, in what Republicans describe as a necessary effort to trim the $1.4 trillion (£858bn) US budget deficit.
'Real spending cuts' Following his meeting with Mr Obama, Mr Boehner said he believed it was important to take time to put through "the largest spending cuts possible to help our economy".
But the House speaker said earlier on Thursday that a disagreement existed "in terms of making real spending cuts" and that talks with the White House were drifting further apart.
"It's really just more of the same. We're going to have real spending cuts. I don't know what some people don't understand about this."
"The issue is ideology, not numbers," Mr Reid said.
He added: "The two main issues that are holding this matter up are reproductive rights and clean air. These matters have no place on a budget bill."
Mr Obama said in an earlier statement he believes "we need to put politics aside and work out our differences" on a spending plan.
Democrats have said the size of the cuts Republicans demand would hinder the nascent US economic recovery.
Republicans in the US House have pushed for $61bn (£37.4bn) in cuts over last year's spending between now and the end of the fiscal year on 30 September, and have sought to use the budget bill to dismantle Democratic policy priorities.