Virginia Gov. Bob McDonnell speaks to the media in front of a statue of George Washington in the rotunda at the Capitol Tuesday in Richmond. (Steve Helber/AP)

Gov. Robert F. McDonnell’s bid to overhaul transportation funding and secure his political legacy prevailed in the GOP-led House on Tuesday but remained in doubt after the evenly divided Senate deadlocked over its version at the midpoint of the General Assembly’s annual session.

As delegates and senators hustled to pass bills from their own chambers before the deadline to send them across the hall, the House gave its blessing to the Republican governor’s $3.1 billion transportation proposal, though not without important changes. At its center remains a plan to eliminate the 17.5-cent gasoline tax — which has not changed since 1987 — and replace it with an increase in the general sales tax, from 5 percent to 5.8 percent.

But the Senate refused to go along. Lt. Gov. Bill Bolling — unable to break a tie in a bill involving revenue — gaveled the day’s nearly eight-hour session to a close after a heated partisan debate.

“The bottom line is, today we have done nothing on transportation,” Republican Senate leader Thomas K. Norment Jr. (James City) said after a final attempt at compromise was voted down.

The Senate then moved to send the bill to the Finance Committee, effectively killing its version and raising doubts about the prospects for the measure on its way over from the House. The House-approved bill is now the only surviving version of the governor’s package, and the Senate could amend or kill it.

“I’m very disappointed,” McDonnell said in telephone interview Tuesday night. “I think the Democrats have a lot of answering to do tonight. They’re going to have to tell us what they’re willing to do. This is a party that says no to everything but higher taxes. I think the Democrats are way out of touch and they need to start being reasonable.”

House Speaker William J. Howell (R-Stafford) expressed disappointment but remained optimistic that a version of the package could still emerge, his spokesman said.

Several Democrats said they objected to the plan on its merits — though their inclination to give the governor’s proposal fair consideration was not helped by the GOP’s stealth maneuver to rewrite the state’s election map.

But even in the House, where McDonnell’s party holds a commanding majority, his transportation plan had a rocky go. Delegates on both sides of the aisle said they disliked elements of the package.

The House added language to prevent the state from setting up tolls on Interstate 95 — the governor has discussed adding tolls in the past, though he did not include tolls in his plan. The House also eliminated McDonnell’s proposed $100 fee on new hybrid cars and allowed for regional transportation projects. What was left would bring in about $52 million less than McDonnell’s bill over five years. The governor’s plan also counts on receiving tax revenue from Internet sales, but that would rely on federal legislation that has been stalled in Congress for several years.

But proponents said the governor’s plan, sponsored by Howell, offered a possible breakthrough, even if it were less than a perfect one.

“Mr. Speaker, there is gridlock in Northern Virginia, and there is gridlock in Hampton Roads, and there is gridlock all over. But the gridlock is caused because of gridlock here in the General Assembly,” Del. Timothy D. Hugo (R-Fairfax) said. “Today is the day, the time is now, and the vote is green. Vote yes.”

But Del. Scott A. Surovell (D-Fairfax) ridiculed the plan as “tea party Twister.”

“It’s a bunch of gymnastics to try to say you’re not raising taxes,” Surovell said. “Beyond that, decoupling road funding from road usage is a pretty radical idea, and it unfairly punishes people who are not even driving on roads.”

As the General Assembly hit the halfway mark of a 45-day session Tuesday, several other measures were put to rest for good this year, including a bid to open parts of Southside Virginia to uranium mining. But the General Assembly also put Virginia on a track to regulate drones, study whether to mint its own currency and prohibit adults from smoking in a car when children are present.

Among the governor’s initiatives, lawmakers appeared most receptive to those aimed at education. McDonnell won approval for new measures that would tighten the accountability of teachers, simplify school ratings by moving to a system of letter grades, and create a new statewide entity with wide-ranging powers to run failing schools.

The bills went through the House with little trouble. In the Senate, Bolling — who irritated fellow Republicans by siding with Democrats who wanted to delay implementing new voter-ID lawsrejoined the GOP fold Tuesday to cast tie-breaking votes on grading schools and establishing the Opportunity Educational Institution to assume control over any school that fails to receive accreditation two years in a row.

True to their word, GOP leadership also steered clear of many of the controversial social issues that overshadowed last year’s session. Measures on abortion and contraceptives failed to advance this year, including several that would have provided that group insurance plans need not cover contraception or abortion-inducing drugs. Democrats tried unsuccessfully to pass a bill that would undo a law enacted last year that that required women to undergo an ultrasound before an abortion.

GOP leadership was also cool to new gun rights legislation. After the murder of 20 children at an elementary school in Newtown, Conn., put guns at the center of national debate, Democrats tried to pass several gun-control measures, such as a ban on assault weapons and high-capacity magazines. None survived, including a compromise for voluntary background checks at gun shows.

The session also has found the governor struggling to keep members of his party in line. The Republican maneuver to redraw the state’s election districts came as much of a surprise to him, he said, as it did to Democrats. McDonnell also objected to a GOP-led plan to distribute electoral-college votes proportionally in presidential elections, saying such a plan would reduce Virginia’s clout. It died in committee.

Despite McDonnell’s assertion that the transportation package was revenue-neutral, some Democrats and some Republicans found themselves agreeing that the package represented a tax hike. Democrats said they did not like it because it was the wrong kind of tax; Republicans did not want any kind of additional taxes.

“It’s because we want smaller government,” said James Parmelee, president of Republicans United for Tax Relief. “We want to spend the revenue we have more wisely.”

Democrats objected to using general-fund revenue on roads that might otherwise go to public safety, education and other programs. Several said the plan also generated too little money for the state’s needs, with even some Republicans from Northern Virginia complaining that the state’s most populous region already receives far less than it sends to Richmond in sales and income taxes and that the imbalance would probably worsen.

“If all we have is sales tax from the Internet sales tax and diversion from the general fund, that bill doesn’t fly,” said House Minority Leader David J. Toscano (D-Charlottesville). “And that’s a lot of what we have right now.”