After missing numerous deadlines, legislators are now targeting the week of Sept. 11 for a possible vote to end the months-long state budget stalemate.

With numerous lawmakers on vacation, officials predicted that a vote on the two-year, $40 billion budget during the month of August would be difficult. The reason is that the Senate is evenly divided at 18-18, and any absences on any given week would prevent 100 percent attendance.

In an email to their Democratic colleagues, House Speaker Joe Aresimowicz and Majority Leader Matt Ritter of Hartford said they want to avoid deeper spending reductions that could come this fall under Gov. Dannel P. Malloy’s executive order. The state has been operating under the executive order since July 1, but millions of dollars in educational cost-sharing funds, for example, have not yet been cut for cities and towns.

“Given the massive cuts that would go into effect in late September/early October, we plan to be in session the week of September 11,’’ they wrote. “To that end, we ask that you involve yourself in the budget process as much as necessary in the coming weeks so that you are prepared to vote that week or earlier. We are committed to moving forward, and we need to be united as a caucus in order to do this.’’

While the 79-member Democratic caucus is trying to show unity in the House, both liberal and conservative members have raised concerns about the budget. Rep. Josh Elliott, one of the chamber’s most liberal Democrats, told The Courant that he is still undecided because the House Democratic budget has deep spending cuts and no income tax increases on the state’s wealthiest citizens. As a vice chairman of the legislature’s tax-writing committee, Elliott has repeatedly said that taxing the wealthy is an important way to help close the state’s projected deficit of $3.5 billion over two years.

“No one wants it to look that we’re not unified,’’ Elliott said. “The more progressive members are going to be forced to come to the middle, even though it seems to me to be unfair. I want to make sure that we’re not the ones who are seen as the bad guys.’’

On the conservative end, Democrats are keenly aware that if four moderate members refuse to vote for the budget, the Democrats would have only 75 votes and could not pass their plan. But Elliott fears that even more members could break away if the final version of the Democratic budget is unpalatable.

“There are about 10 or 11 of our colleagues who would be willing to sign up with the Republican budget if it came to that,’’ Elliott said.

Although the state’s fiscal year started on July 1, lawmakers have been unable to reach a compromise as some Democrats are pushing for tax increases and Republicans are pushing for more spending cuts. So far, Democrats have been unable to cobble together a majority in either the House and Senate.